Tree Graph Research Articles

Predicting the Health Insurance Premium by Analyzing the Customer Feature Importance with Random Forest

This research aims to predict the Heath care Insurance Premi by analyzing the customer characteristics Random Forest Algorithm. Secondly, this research will determine feature importance from customer characteristics that drive the closing decision. This research methodology is quantitative, and data mining methodology and data will be derived from primary data, and 202 data will be processed and cleaned into 148 data. This research also uses supervisory learning and using the random forest algorithm. The novelty of this research, Firstly, the health care insurance premium can be predicted by the machine learning random forest algorithm. Secondly, the sequence of importance from the customer characteristics can be determined by the feature of importance function at the random forest. A random forest algorithm can predict the prospect data test with an accurate value of 63,33 %. First, the crucial question that has to be made is how much the income is; second is age, is between 45-55 years old, and the third is how many dependent. The decision tree graph helps construct the questioner's level, leading to a monthly target premium of 3 million to 5 million. Keywords: Health care Insurance Premi Prediction, Random forest Algorithm, The feature Importance.

CENOTIC ROLE OF INFECTIOUS DISEASES IN ABIES SIBIRICA LEDEB. STANDS IN THE SOUTH CENTRAL SIBERIA

Background. Degradation of Abies sibirica Ledeb.-dominated forests in the South Central Siberia is a reflection of the global trend of coniferous forest ecosystems decline. Nevertheless, the role of infectious diseases in coniferous forests degradation and dieback is often underestimated.
 Research aim. To assess the coenotic role of infectious diseases in fir-dominated stands in the South Central Siberia, considering the differentiation in trees.
 Materials and methods. The research was based on a survey of A. sibirica-dominated forest stands growing in Biryusinsky forest management unit of the Krasnoyarsk Krai government-owned publicly funded “Emelyanovskoye forestry”. Research methods included a detailed (instrumental) forest pathological examination, macroscopic diagnostics of tree diseases, graph analytics and statistical analysis of tree diameter distribution series, evaluation of disease manifestation indicators.
 Results. Stem rot and fir broom rust are typical diseases increasing the risk of windsnap and trees weakening. The prevalence of fir broom rust was over 10%. Rust fungus intermediate hosts in the forest floor determine the degree of damage to a stand. Fir broom rust randomly affected trees of different age and diameters. The bacterial blight in fir forests mainly affected trees of I-II Kraft classes causing their gradual dying. The bacterial blight in the study area was of low infection degree (up to 20%). The most dangerous was the root rot caused by Armillaria mellea s.l. that affected trees of different cenotic roles causing their group dieback.
 Conclusion. Dendropathogenic organisms are an important endogenous factor influencing the state of dark coniferous forests with a predominance of A. sibirica in the South Central Siberia. Their cenotic role is unequal. The most significant are pathogens causing necrosis and cancer diseases, and especially the root pathogen A. mellea, which leads to weakening and dying of a large number of trees of different status in the stand structure.

GRAPH TANGGA DAN SIFAT-SIFATNYA

Ladder Graph is one type of connected and simple graph that has its own uniqueness. The aim of this research is to find the k-deficiency of points in the spanning tree in the ladder graph. Calculation of k-deficiency is carried out for each additional step, starting from the second ladder ( L2), up to the nth Ladder (Ln). Calculations are based on a representative spanning tree on each ladder. In the end, we get a number pattern from the second ladder onwards which is then proven by mathematical induction, for the calculation of each step up the ladder. In this study, the pattern of k-deficiency points on the ladder graph was obtained.

The Complexity of the Super Subdivision of Cycle-Related Graphs Using Block Matrices

The complexity (number of spanning trees) in a finite graph Γ (network) is crucial. The quantity of spanning trees is a fundamental indicator for assessing the dependability of a network. The best and most dependable network is the one with the most spanning trees. In graph theory, one constantly strives to create novel structures from existing ones. The super subdivision operation produces more complicated networks, and the matrices of these networks can be divided into block matrices. Using methods from linear algebra and the characteristics of block matrices, we derive explicit formulas for determining the complexity of the super subdivision of a certain family of graphs, including the cycle Cn, where n=3,4,5,6; the dumbbell graph Dbm,n; the dragon graph Pm(Cn); the prism graph Πn, where n=3,4; the cycle Cn with a Pn2-chord, where n=4,6; and the complete graph K4. Additionally, 3D plots that were created using our results serve as illustrations.

On the P3-Coloring of Bipartite Graphs

The advancement in coloring schemes of graphs is expanding over time to solve emerging problems. Recently, a new form of coloring, namely P3-coloring, was introduced. A simple graph is called a P3-colorable graph if its vertices can be colored so that all the vertices in each P3 path of the graph have different colors; this is called the P3-coloring of the graph. The minimum number of colors required to form a P3-coloring of a graph is called the P3-chromatic number of the graph. The aim of this article is to determine the P3-chromatic number of different well-known classes of bipartite graphs such as complete bipartite graphs, tree graphs, grid graphs, and some special types of bipartite graphs. Moreover, we have also presented some algorithms to produce a P3-coloring of these classes with a minimum number of colors required.

Completely Independent Spanning Trees in Line Graphs

Completely Independent Spanning Trees in Line Graphs

Skeleton Graph-Based Ultrasound-CT Non-Rigid Registration

Autonomous ultrasound (US) scanning has attracted increased attention, and it has been seen as a potential solution to overcome the limitations of conventional US examinations, such as inter-operator variations. However, it is still challenging to autonomously and accurately transfer a planned scan trajectory on a generic atlas to the current setup for different patients, particularly for thorax applications with limited acoustic windows. To address this challenge, we proposed a skeleton graph-based non-rigid registration to adapt patient-specific properties using subcutaneous bone surface features rather than the skin surface. To this end, the self-organization mapping is successively used twice to unify the input point cloud and extract the key points, respectively. Afterward, the minimal spanning tree is employed to generate a tree graph to connect all extracted key points. To appropriately characterize the rib cartilage outline to match the source and target point cloud, the path extracted from the tree graph is optimized by maximally maintaining continuity throughout each rib. To validate the proposed approach, we manually extract the US cartilage point cloud from one volunteer and seven CT cartilage point clouds from different patients. The results demonstrate that the proposed graph-based registration is more effective and robust in adapting to the inter-patient variations than the ICP (distance error mean <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\pm$</tex-math></inline-formula> SD: <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$5.0\pm \rm{1.9}~mm$</tex-math></inline-formula> vs <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$8.6\pm \rm{6.7}~mm$</tex-math></inline-formula> on seven CTs).

Penerapan Algoritma Batchelor-Wilkins dalam Pengklasteran Graf

Batchelor-Wilkins Algorithm is a simple and heuristic clustering algorithm used when the number of classes is unknown. In this paper we will use Batchelor-Wilkins algorithm in graph clustering, specifically a Banana Tree Graph B(n,k), a graph obtained by connecting one leaf of each of n copies of a complete bipartite graph K_{1,k-1} to a single root vertex.

On Weighted Vertex and Edge Mostar Index for Trees and Cacti with Fixed Parameter

It was introduced by Doˇsli ́c and Ivica et al. (Journal of Mathematical chemistry, 56(10) (2018): 2995–3013), as an innovative graph-theoretic topological identifier, the Mostar index is significant in simulating compounds’ thermodynamic properties in simulations, which is defined as sum of absolute values of the differences among nu(e|Ω) and nv(e|Ω) over all lines e = uv ∈ Ω, where nu(e|Ω) (resp. nv(e|Ω)) is the collection of vertices of Ω closer to vertex u (resp. v) than to vertex v (resp. u). Let C(n, k) be the set of all n-vertex cacti graphs with exactly k cycles and T(n, d) be the set of all n-vertex tree graphs with diameter d. It is said that a cacti is a connected graph with blocks that comprise of either cycles or edges. Beginning with the weighted Mostar index of graphs, we developed certain transformations that either increase or decrease index. To advance this analysis, we determine the extreme graphs where the maximum and minimum values of the weighted edge Mostar index are accomplished. Moreover, we compute the maximum weighted vertex Mostar invariant for trees with order n and fixed diameter d.

Pk-factors in squares and line graphs of trees

A Pk-factor H of G is a spanning subgraph of G such that each component of H is a path of k vertices, where k≥2. In this paper, we obtain two necessary conditions for Pk-factors in the squares and line graphs of trees, respectively. It is shown that the results are best possible in some sense. Furthermore, we give a characterization for a class of trees whose line graphs contain P4-factors.

Spider Web Graphs

Recent results from Chih-Scull show that the ×-homotopy relation on finite graphs can be expressed via a sequence of “spider moves” which shift a single vertex at a time. In this paper we study a “spider web graph” which encodes exactly these spider moves between graph homomorphisms. We show how composition of graph homomorphisms relate to the spider web, study the components of spider webs for bipartite and tree graphs, andfinish by giving an explicit description of the spider web for homomorphisms from a bipartite graph to a star graph.

Two completely independent spanning trees of split graphs

G is a split graph if V(G) can be partitioned into a clique D and an independent set I. Let τ(G) denote the toughness of a graph G. If a graph G contains two spanning trees T1,T2 such that for each two distinct vertices x,y of G, the (x,y)-path in each Ti has no common edge and no common vertex except for the two ends, then T1,T2 are called two completely independent spanning trees (CISTs) of G,i∈{1,2}. Several results have shown that some sufficient conditions for Hamiltonian graphs also guarantee the existence of two CISTs, which implies the Hamiltonicity and the existence of two CISTs of a graph have close connection. In this paper, we prove that if G is a Hamiltonian split graph with |D|>max{3,|I|}, then G contains two CISTs. Moreover, we show that if G is a Hamiltonian split graph with τ(G)>1, then G contains two CISTs. As a corollary, we obtain that every 32-tough split graph contains two CISTs.

Line graphs of trees with the largest eigenvalue multiplicity

Let T be a tree with p≥3 pendant edges and let L(T) be its line graph. In this paper, we prove the multiplicity of an arbitrary adjacency eigenvalue of L(T) is no larger than p−1. Furthermore, the line graphs L(T) of trees which contain an adjacency eigenvalue with multiplicity p−1 are completely determined.

A Unified Approach for Extremal General Exponential Multiplicative Zagreb Indices

The study of the maximum and minimal characteristics of graphs is the focus of the significant field of mathematics known as extreme graph theory. Finding the biggest or smallest graphs that meet specified criteria is the main goal of this discipline. There are several applications of extremal graph theory in various fields, including computer science, physics, and chemistry. Some of the important applications include: Computer networking, social networking, chemistry and physics as well. Recently, in 2021 exponential multiplicative Zagreb indices were introduced. In generalization, we introduce the generalized form of exponential multiplicative Zagreb indices for α∈R+\{1}. Furthermore, to see the behaviour of generalized first and second exponential Zagreb indices for α∈R+\{1}, we used a transformation method. In term of the two newly developed generalized exponential multiplicative Zagreb indices, we will investigate the extremal bicyclic, uni-cyclic and trees graphs. Four graph transformations are used and some bounds are presented in terms of generalized exponential multiplicative Zagreb indices.

Oriented spanning trees and stationary distribution of digraphs

By using biclique partitions of digraphs, this paper gives reduction formulas for the number of oriented spanning trees, stationary distribution vector and Kemeny's constant of digraphs. As applications, we give a method for enumerating spanning trees of undirected graphs by vertex degrees and biclique partitions. The biclique partition formula also extends the results of Knuth and Levine from line digraphs to general digraphs.

Haplotype Disequilibrium in the TLR Genes of Czech Red Pied Cattle

Hybrid resequencing of the antibacterial innate immune genes coding for toll-like receptors, namely TLR1, TLR2, TLR4, TLR5, and TLR6, using HiSeq and PacBio technologies of pooled population samples of Czech Simmental (Czech Red) cattle allowed us to determine haplotypes formed by the polymorphisms present. Directly determined haplotypes within the range of the large proximal amplicon in TLR2 formed two clusters in the network tree graph. The distribution of the statistically reconstructed haplotypes based on individual genotyping of the present SNPs was consistent. Similarly, the statistically reconstructed haplotypes in TLR5 and TLR6 formed two clusters. The trend of bimodal distribution was also observed in TLR4, while the limited diversity of TLR1 did not allow for any conclusion. The observed bimodal distribution is consistent with earlier reports for cattle populations worldwide. The stability of this phenomenon cannot be ascribed to historical origin but rather to a long-term effect of balancing selection. The equilibrium might be based on two different essential functions performed by the TLR genes or their products. The formation of two kinds of heterodimers by the TLR2 product, namely, TLR2/TLR1 and TLR2/TLR6 with different ligand specificities, is considered to be a particular case. On the other hand, the better expression of the bimodal groups in the 5′-proximal SNPs supports the localization of the selection targets in the upstream regulatory regions or the functional interactions in the proximal part of the transcripts.

Multiagent MST Cover: Pleasing All Optimally via a Simple Voting Rule

Given a connected graph on whose edges we can build roads to connect the nodes, a number of agents hold possibly different perspectives on which edges should be selected by assigning different edge weights. Our task is to build a minimum number of roads so that every agent has a spanning tree in the built subgraph whose weight is the same as a minimum spanning tree in the original graph. We first show that this problem is NP-hard and does not admit better than ((1-o(1)) ln k)-approximation polynomial-time algorithms unless P = NP, where k is the number of agents. We then give a simple voting algorithm with an optimal approximation ratio. Moreover, our algorithm only needs to access the agents' rankings on the edges. Finally, we extend our problem to submodular objective functions and Matroid rank constraints.

HGAT: smart contract vulnerability detection method based on hierarchical graph attention network

With the widespread use of blockchain, more and more smart contracts are being deployed, and their internal logic is getting more and more sophisticated. Due to the large false positive rate and low detection accuracy of most current detection methods, which heavily rely on already established detection criteria, certain smart contracts additionally call for human secondary detection, resulting in low detection efficiency. In this study, we propose HGAT, a hierarchical graph attention network-based detection model, in order to address the aforementioned issues as well as the shortcomings of current smart contract vulnerability detection approaches. First, using Syntax Tree (AST) and Control Flow Graph, the functions in the smart contract are abstracted into code graphs (CFG). Then abstract each node in the code subgraph, extract the node features, utilize the graph attention mechanism GAT, splice the obtained vectors to form the features of each line of statements and use these features to detect smart contracts. To create test data and assess HGAT, we leverage the open-source smart contract vulnerability sample dataset. The findings of the experiment indicate that this method can identify smart contract vulnerabilities more quickly and precisely than other detection techniques.

The Complexity of Wheel Graphs with Multiple Edges and Vertices

In this paper, we focus on calculate the number of spanning trees of the general wheel graphs, which meansthe original wheel graphs adding large amount of vertices and edges. Particularly, we introduce the C-graphand deduce a new equation that computing the spanning trees by removing C-graphs instead of edges.In Addition, we test our results by Kirchhoff’s matrix-tree theorem in some simple cases and provide thetree entropy of the general wheel graphs. Finally, we analyse the relation between the wheel graph anddouble-wheel graphs and propose the idea of calculating the spanning trees of double-wheel graphs.

Scaling properties of RNA as a randomly branching polymer.

Formation of base pairs between the nucleotides of a ribonucleic acid (RNA) sequence gives rise to a complex and often highly branched RNA structure. While numerous studies have demonstrated the functional importance of the high degree of RNA branching-for instance, for its spatial compactness or interaction with other biological macromolecules-RNA branching topology remains largely unexplored. Here, we use the theory of randomly branching polymers to explore the scaling properties of RNAs by mapping their secondary structures onto planar tree graphs. Focusing on random RNA sequences of varying lengths, we determine the two scaling exponents related to their topology of branching. Our results indicate that ensembles of RNA secondary structures are characterized by annealed random branching and scale similarly to self-avoiding trees in three dimensions. We further show that the obtained scaling exponents are robust upon changes in nucleotide composition, tree topology, and folding energy parameters. Finally, in order to apply the theory of branching polymers to biological RNAs, whose length cannot be arbitrarily varied, we demonstrate how both scaling exponents can be obtained from distributions of the related topological quantities of individual RNA molecules with fixed length. In this way, we establish a framework to study the branching properties of RNA and compare them to other known classes of branched polymers. By understanding the scaling properties of RNA related to its branching structure, we aim to improve our understanding of the underlying principles and open up the possibility to design RNA sequences with desired topological properties.