Set Of Graphs Research Articles

Super Hyper Dominating and Super Hyper Resolving on Neutrosophic Super Hyper Graphs and Their Directions in Game Theory and Neutrosophic Super Hyper Classes

In this research article, the notions of Super Hyper Dominating and Super Hyper Resolving are defined in the setting of neutrosophic Super Hyper Graphs. Some ideas are introduced on both notions of Super Hyper Dominating and Super Hyper Resolving, simultaneously and as the same with each other. Some neutrosophic Super Hyper Classes are defined based on the notion, Super Hyper Resolving. The terms of duality, totality, perfectness, connectedness, and stable, are added to basic framework and initial notions, Super Hyper Dominating and Super Hyper Resolving but the concentration is on the “perfectness” to figure out what’s going on when for all targeted Super Hyper Vertices, there’s only one Super Hyper Vertex in the intended set. There are some instances and some clarifications to make sense about what’s happened and what’s done in the starting definitions. The key point is about the minimum sets. There are some questions and some problems to be taken as some avenues to pursue this study and this research. A basic familiarity with Super Hyper Graph theory and neutrosophic Super Hyper Graph theory is proposed.

Analytical transformations software for stationary modes of induction motors and electric drives

<span lang="EN-US">A program was developed in the package of symbolic transformations Maple. It provides automatic analytical transformation and derivation of formulas and plotting of the main characteristics of induction motors (IM) in a convenient form for an electrical engineer and student: torque=f(slip) T=f(s), angular speed=f(Torque) ω=f(T), angular speed=f(Current) ω=f(I), current=f(slip) I=f(s); cos(φ) and phase angle (phi) φ for stator currents and rotor currents, and magnetizing circuit, machine efficiency η=f(s) and a number of other characteristics. The calculation is based on the equivalent circuit of IM motors in its different variants: with one cage in the rotor, with two or more cages in the rotor, taking into account the skin effect in the rotor rods and without it. The user can build up the equivalent circuit to the desired configuration. The algorithm of further transformations is based on analytical obtaining of amplitude/frequency and phase/frequency characteristics in the nodes of the equivalent circuits with further calculation by power and slip. Online animation of the graphs with alternate variations of all resistances R and inductances L values of the model is provided. The article contains screenshots of important parts of the programs and illustrates the complete set of graphs.</span>

Developing A Secure Cryptosystem with Rainbow Vertex Antimagic Coloring of Cycle Graph

An edge labeling of graph G is a function g from the edge set of graph G to the first natural numbers up to the number of the edge set. Graph G admits a rainbow vertex antimagic coloring if, for any two vertices, there is a path with different colors of all internal vertices. The vertex color of graph G is assigned by vertex weight. The vertex weight of graph G is obtained by summing all edge labels that incident with that vertex. The rainbow vertex antimagic connection number of graph G, denoted by rvac(G) is the smallest number of different colors induced by rainbow vertex antimagic coloring. In this research, we determine the upper bound of the rainbow vertex antimagic connection number (rvac) on a cycle graph (Cn) and create a secured cryptosystem using a modified Affine Cipher based on rainbow vertex antimagic coloring.

On a conjecture of spectral extremal problems

For a simple graph F, let Ex(n,F) and Exsp(n,F) denote the set of graphs with the maximum number of edges and the set of graphs with the maximum spectral radius in an n-vertex graph without any copy of the graph F, respectively. The Turán graph Tn,r is the complete r-partite graph on n vertices where its part sizes are as equal as possible. Cioabă, Desai and Tait [The spectral radius of graphs with no odd wheels, European J. Combin., 99 (2022) 103420] posed the following conjecture: Let F be any graph such that the graphs in Ex(n,F) are Turán graphs plus O(1) edges. Then Exsp(n,F)⊂Ex(n,F) for sufficiently large n. In this paper we consider the graph F such that the graphs in Ex(n,F) are obtained from Tn,r by adding O(1) edges, and prove that if G has the maximum spectral radius among all n-vertex graphs not containing F, then G is a member of Ex(n,F) for n large enough. Then Cioabă, Desai and Tait's conjecture is completely solved. Furthermore, we give a stronger result.

On strong avoiding games

Given an increasing graph property F, the strong Avoider-Avoider F game is played on the edge set of a complete graph. Two players, Red and Blue, take turns in claiming previously unclaimed edges with Red going first, and the player whose graph possesses F first loses the game. If the property F is “containing a fixed graph H”, we refer to the game as the H game.We prove that Blue has a winning strategy in two strong Avoider-Avoider games, P4 game and CC>3 game, where CC>3 is the property of having at least one connected component on more than three vertices.We also study a variant, the strong CAvoider-CAvoider games, with additional requirement that the graph of each of the players must stay connected throughout the game. We prove that Blue has a winning strategy in the strong CAvoider-CAvoider games S3 and P4, as well as in the Cycle game, where the players aim at avoiding all cycles.

On a conjecture about the spectral radius of block graphs

Let Bn,q be the set of all block graphs with n vertices and all blocks on q+1 vertices for every q≥2. In this paper, we determine the unique graph in Bn,q that attains the minimum spectral radius. This solves a conjecture posted by Conde et al. (2022) [4].

The Average Size of Independent Sets in Unicyclic Graphs

The Average Size of Independent Sets in Unicyclic Graphs

Isostructural Crystals of Bis(Guanidinium) Trioxofluoro-Phosphate/Phosphite in the Ratio 1/0, 0.716/0.284, 0.501/0.499, 0.268/0.732, 0/1—Crystal Structures, Vibrational Spectra and Second Harmonic Generation

The title structures of bis(guanidinium) trioxofluorophosphate, bis(guanidinium) trioxofluorophosphate-phosphite (0.716/0.284), bis(guanidinium) trioxofluorophosphate-phosphite (0.501/0.499), bis(guanidinium) trioxofluorophosphate-phosphite (0.268/0.732), and bis(guanidinium) phosphite are crystal-chemically isotypic. Their structures correspond to the structure of bis(guanidinium) trioxofluorophosphate which was determined by Prescott, Troyanov, Feist & Kemnitz (Z. Anorg. Allg. Chem. 2002, 628, 1749–1755). The P and O atoms of the substituted trioxofluorophosphate and phosphite anions share the same positions while the P-F and P-Hhydrido are almost parallel and oriented in the same direction. Two symmetry-independent anions and two of three symmetry-independent cations are situated on the crystallographic mirror planes. The ions are interconnected by N-H⋯O hydrogen bonds of moderate strength. The most frequent graph set motif is R22(8), which involves interactions between the primary amine groups and the trioxofluorophosphate or phosphite O atoms. Fluorine, as well as the hydrido hydrogen, avoids inclusion into the hydrogen-bond network. The Hirshfeld surface analysis was also performed for the comparison of intermolecular interactions in the title structures of bis(guanidinium trioxofluorophosphate and bis(guanidinium) phosphite. The title crystals were also characterized by vibrational spectroscopy methods (FTIR and Raman) and the second harmonic generation (SHG). The relative SHG efficiency considerably decreases from bis(guanidinium) trioxofluorophosphate to bis(guanidinium) phosphite for the fundamental 1064 nm laser line.

Deep graph level anomaly detection with contrastive learning

Graph level anomaly detection (GLAD) aims to spot anomalous graphs that structure pattern and feature information are different from most normal graphs in a graph set, which is rarely studied by other researchers but has significant application value. For instance, GLAD can be used to distinguish some different characteristic molecules in drug discovery and chemical analysis. However, GLAD mainly faces the following three challenges: (1) learning more comprehensive graph level representations to differ normal graphs and abnormal graphs, (2) designing an effective graph anomaly evaluation paradigm to capture graph anomalies from the local and global graph perspectives, (3) overcoming the number imbalance problem of normal and abnormal graphs. In this paper, we combine graph neural networks and contrastive learning to build an end-to-end GLAD framework for solving the three challenges above. We aim to design a new graph level anomaly evaluation way, which first utilizes the contrastive learning strategy to enhance different level representations of normal graphs from node and graph levels by a graph convolution autoencoder with perturbed graph encoder. Then, we evaluate the error of them with corresponding representations of the generated reconstruction graph to detect anomalous graphs. Extensive experiments on ten real-world datasets from three areas, such as molecular, protein and social network anomaly graphs, show that our model can effectively detect graph level anomaly from the majority and outperform existing advanced methods.

On Critical Unicyclic Graphs with Cutwidth Four

The cutwidth minimization problem consists of finding an arrangement of the vertices of a graph G on a line Pn with n=|V(G)| vertices in such a way that the maximum number of overlapping edges (i.e., the congestion) is minimized. A graph G with a cutwidth of k is k-cutwidth critical if every proper subgraph of G has a cutwidth less than k and G is homeomorphically minimal. In this paper, we first verified some structural properties of k-cutwidth critical unicyclic graphs with k>1. We then mainly investigated the critical unicyclic graph set T with a cutwidth of four that contains fifty elements, and obtained a forbidden subgraph characterization of 3-cutwidth unicyclic graphs.

Bridge-Depth Characterizes which Minor-Closed Structural Parameterizations of Vertex Cover Admit a Polynomial Kernel

We study the kernelization complexity of structural parameterizations of the Vertex Cover problem. Here, the goal is to find a polynomial-time preprocessing algorithm that can reduce any instance $(G,k)$ of the Vertex Cover problem to an equivalent one, whose size is polynomial in the size of a predetermined complexity parameter of $G$. A long line of previous research deals with parameterizations based on the number of vertex deletions needed to reduce $G$ to a member of a simple graph class $\mathcal{F}$, such as forests, graphs of bounded tree-depth, and graphs of maximum degree two. We set out to find the most general graph classes $\mathcal{F}$ for which Vertex Cover parameterized by the vertex-deletion distance of the input graph to $\mathcal{F}$ admits a polynomial kernelization. We give a complete characterization of the minor-closed graph families $\mathcal{F}$ for which such a kernelization exists. We introduce a new graph parameter called bridge-depth, and prove that a polynomial kernelization exists if and only if $\mathcal{F}$ has bounded bridge-depth. The proof is based on an interesting connection between bridge-depth and the size of minimal blocking sets in graphs, which are vertex sets whose removal decreases the independence number.

Ab Initio Study of H-Bond Dynamics in Three-Component Crystals Comprising (DABCOH+ )n Polycationic Chains.

In this work, the dynamic character of hydrogen-bond (H-bond) networks in two three-component crystals comprising polycationic chains was described. The first studied system was 1,4-diazabicyclo[2.2.2]octan-1-ium (DABCOH+ ) sulfamate monohydrate, known for its large negative linear compressibility. The second analyzed material was the newly obtained polar salt co-crystal: 1,4-diazabicyclo[2.2.2]octan-1-ium sulfamate urea. X-ray diffraction measurements enabled us to study the H-bond systems in both crystals using the graph set analysis. Obtained structures served as the initial models for Born-Oppenheimer molecular dynamics computations. A detailed study of intermolecular interactions and power spectra was conducted. The analysis of time and space correlations between the changes in H-bonds enabled the detection of proton transfer occurring in both systems at 300 K. Further study of those dynamic phenomena was done using the Energy Decomposition Analysis for selected trajectory fragments. Our work should improve the understanding of dielectric and ferroelectric properties of hybrid organic-inorganic materials.

Crystal structure of vismodegib, C19H14Cl2N2O3S

The crystal structure of vismodegib has been solved and refined using synchrotron X-ray powder diffraction data, and optimized using density functional theory techniques. Vismodegib crystallizes in space group P21/a (#14) with a = 16.92070(20), b = 10.20235(4), c = 12.16161(10) Å, β = 108.6802(3)°, V = 1988.873(9) Å3, and Z = 4. The crystal structure consists of corrugated layers of molecules parallel to the bc-plane. There is only one classical hydrogen bond in the structure, between the amide nitrogen atom and the N atom of the pyridine ring. Pairs of these hydrogen bonds link the molecules into dimers, with a graph set R2,2(14) > a > a. The powder pattern has been submitted to ICDD for inclusion in the Powder Diffraction File™ (PDF®).

On analysis of heat of formation and entropy measures for indium phosphide

A chemical graph represents a chemical or molecular compound in the form of a graph. The vertex set of the chemical graph contains the atoms or molecules of the compound while the edge set comprises of the bonding between the molecules or atoms. In this paper, we compute various connectivity indices based on degrees of vertices of chemical graph of Indium Phosphide (InP) including general Randić, hyper Zagreb and redefined Zagreb indices etc. Afterwards, we calculate the physical measures such as entropy and heat of formation of InP. We fit curves between different indices and the thermodynamical properties namely heat of formation and entropy by using MATLAB through different methods based on linearity and non-linearity. The performance of the method is tested using root mean square error, the sum of squared errors or R 2 . Furthermore, we give graphical representations of these indices. These mathematical frameworks might provide a way to study the thermodynamical properties of the chemical structure of InP at different conditions which will assist to comprehend the relationship between system dimension and these measures.

Locating Hop Sets in a Graph

Let G be a connected graph with vertex set V (G) and edge set E(G). The open hop neighborhood of vertex v ∈ V (G) is the set NG(v, 2) = {w ∈ V (G) : dG(v, w) = 2}, where dG(v, w) denotes the distance between v and w. A non-empty set S ⊆ V (G) is a locating hop set of G if NG(u, 2) ∩ S ̸= NG(v, 2) ∩ S for every pair of distinct vertices u, v ∈ V (G) \ S. The smallest cardinality of a locating hop set of G, denoted by lhn(G) is called the locating hop number of G. This study focuses mainly on the concept of locating hop set in graphs. Characterizations of locating hop sets in the join and corona of two graphs are given and bounds for the corresponding locating hop numbers of these graphs are determined.

Outer-connected Hop Dominating Sets in Graphs

Let G be an undirected graph with vertex and edge sets V (G) and E(G), respectively. A hop dominating set S ⊆ V (G) is called an outer-connected hop dominating set if S = V (G) or the subgraph ⟨V (G) \ S⟩ induced by V (G) \ S is connected. The minimum size of an outer-connected hop dominating set is the outer-connected hop domination number γfch(G). A dominating setof size γfch(G) of G is called a γfch-set. In this paper, we investigate the concept and study it for graphs resulting from some binary operations. Specifically, we characterize the outer-connected hop dominating sets in the join, corona and lexicographic products of graphs, and determine bounds of the outer-connected hop domination number of each of these graphs.

Forcing Subsets of Connected Co-Independent Hop Domination in the Join and Corona of Graphs

This study deals with the forcing subsets of a minimum connected co-independent hop dominating sets in graphs. Bounds or exact values of the forcing connected co-independent hop domination numbers of graphs resulting from some binary operations such asjoin and corona of graphs are determined.Some main results generated in this study include characterization of the minimum connected co-independent hop dominating sets, characterization of the forcing subsets for these types of sets, and bounds or exact values of the forcing connected co-independent hop domination numbers of the join and corona of graphs.

Forcing Subsets of Connected Co-Independent Hop Domination in the Edge Corona and Lexicographic Product of Graphs

This study deals with the forcing subsets of a minimum connected co-independent hop dominating sets in graphs. Bounds or exact values of the forcing connected co-independent hop domination numbers of graphs resulting from some binary operations such asedge corona and lexicographic product of graphs are determined.Some main results generated in this study include: (a) characterization of the minimum connected co-independent hop dominating sets; and (b) characterization of the forcing subsets for these types of sets.

Hop Independent Hop Domination in Graphs

Let G be an undirected graph with vertex and edge sets V (G) and E(G), respectively. A set S ⊆ V (G) is called a hop independent hop dominating set of G if S is both hop independent and hop dominating set of G. The minimum cardinality of hop independent hop dominating set of G, denoted by γhih(G), is called the hop independent hop domination number of G. In this paper, we show that the hop independent hop domination number of a graph G lies between the hop domination number and the hop independence number of graph G. We characterize these types of sets in the shadow graph, join, corona, and lexicographic product of two graphs. Moreover, either exact values or bounds of the hop independent hop domination numbers of these graphs are given.

On 2-Resolving Hop Dominating Sets in the Join, Corona and Lexicographic Product of Graphs


 
 
 
 Let G be a connected graph. A set S of vertices in G is a 2-resolving hop dominating set of G if S is a 2-resolving set in G and for every vertex x ∈ V (G)\S there exists y ∈ S such that dG(x, y) = 2. The minimum cardinality of a set S is called the 2-resolving hop domination number of G and is denoted by γ2Rh(G). This study aims to combine the concept of hop domination with the 2-resolving sets of graphs. The main results generated in this study include the characterization of 2-resolving hop dominating sets in the join, corona and lexicographic product of two graphs, as well as their corresponding bounds or exact values.