Windmill Graph Research Articles

On Some Topological, Reciprocal Indices and Polynomials of Line Graph of Dutch Windmill Graph

On Some Topological, Reciprocal Indices and Polynomials of Line Graph of Dutch Windmill Graph

The Degree-Topology of CertainTypes of Graphs and PT0-Space

This work aimed to study the degree topology of certain types of graphs namely, the wheel, helm, gear, pan, tadpole, and windmill graphs, respectively. In addition, a new separation axiom known as -space that joins the topological space and paths in the graph is introduced. Also, the relation between -space and the degree-topology of the connected and disconnected graph was stydied. Moreover, many examples were studied in new separation space.

On the Square Free Detour Number of Windmill Graphs

On the Square Free Detour Number of Windmill Graphs

Monitoring Edge-Geodetic Numbers of Some Networks

Motivated by the problem of network monitoring, Foucaud, Krishna and Ramasubramony Sulochana introduced the concept of monitoring edge-geodetic set and a related graph invariant. A monitoring edge-geodetic set (MEG-set for short) is a set such that the removal of any edge changes the distance between some pair of vertices in the set. The minimum size of the monitoring edge-geodetic set is called the monitoring edge-geodetic number. In this paper, we study the monitoring edge-geodetic numbers of some well-known networks, including folded hypercube, folded [Formula: see text]-cube, prism graph, anti-prism graph, Jahangir graph and windmill graphs.

On Super (a,d)-C_3- Antimagic Total Labeling of Dutch Windmill Graph D_3^m

This paper is aimed to investigate the existence of super (a,d)-C_3- antimagic total labeling of dutch windmill graph D_3^m . The methods to achieves the goal was taken in three step. First of all determine the edge and vertices notation on dutch windmill graph . At the second step, labeling the vertices and edges of several dutch windmill graphs, then obtained the pattern. Finally pattern must be proven to become theorem. Based on the study, The Dutch Windmill Graph D_3^m, with m>=2 has super (14m+9,5)-C_3- antimagic total labeling, super (13m+8,3)-C_3- antimagic total labeling, super (12m+9.,5)-C_3- antimagic total labeling, super (11m+10.,7)-C_3- antimagic total labeling, super (10m+8.,3)-C_3- antimagic total labeling.

An Inclusive Local Irregularity Vertex Coloring of Dutch Windmill Graph

Let G(V,E) is a simple and connected graph with V(G) as vertex set and E(G) as edge set. An inclusive local irregularity vertex coloring is a development of the topic of local irregularity vertex coloring. An inclusive local irregularity vertex coloring is defined by coloring the graph so that its weight value is obtained by adding up the labels of the neighboring vertex and its label. The inclusive local irregularity chromatic number is defined as the minimum number of colors obtained from coloring the vertex of the inclusive local irregularity in graph G. In this paper, we find the inclusive local irregularity vertex coloring and determine the chromatic number on the Dutch windmill graph using axiomatic deductive and pattern recognition methods. The results of this study are expected to be used as a basis for studies in the development of knowledge related to the inclusive local irregularity vertex coloring

GOURAVA DOMINATION INDICES OF GRAPHS

In this paper, we introduce the first and second Gourava domination indices and their corresponding polynomials of a graph. Furthermore, we compute these indices and their corresponding polynomials for some standard graphs, French windmill graphs, friendship graphs and book graphs.

MODIFIED DOMINATION SOMBOR INDEX AND ITS EXPONENTIAL OF A GRAPH

In this paper, we introduce the modified domination Sombor index and its corresponding exponential of a graph. Also we introduce the domination Sombor exponential of a graph. We compute the modified domination Sombor index and its corresponding exponential for some standard graphs, French windmill graphs, friendship graphs and book graphs. Furthermore, we establish some properties of the domination Sombor index

DOMINATION NIRMALA INDICES OF GRAPHS

In this study, we introduce the domination Nirmala index, modified domination Nirmala index and their corresponding exponentials of a graph.Furthermore, we compute these domination Nirmala indices for some standard graphs, windmill graphs, book graphs.

Symmetry-Adapted Domination Indices: The Enhanced Domination Sigma Index and Its Applications in QSPR Studies of Octane and Its Isomers

Molecular descriptors are essential in mathematical chemistry for studying quantitative structure–property relationships (QSPRs), and topological indices are a valuable source of information about molecular properties, such as size, cyclicity, branching degree, and symmetry. Graph theory has played a crucial role in the development of topological indices and dominating parameters for molecular descriptors. A molecule graph, under graph isomorphism conditions, represents an invariant number, and the graph theory approach considers dominating sets, which are subsets of the vertex set where every vertex outside the set is adjacent to at least one vertex inside the set. The dominating sigma index, a topological index that incorporates the mathematical principles of domination topological indices and the sigma index, is applicable to some families of graphs, such as book graphs and windmill graphs, and some graph operations, which have exact values for this new index. To evaluate the effectiveness of the domination sigma index in QSPR studies, a comparative analysis was conducted to establish an appropriate domination index that correlates with the physicochemical properties of octane and its isomers. Linear and non-linear models were developed using the QSPR approach to predict the properties of interest, and the results show that both the domination forgotten and domination first Zagreb indices exhibited satisfactory performance in comparison testing. Further research into QSAR/QSPR domination indices is required to build more robust models for predicting the physicochemical properties of organic compounds while maintaining the importance of symmetry.

Embedding Augmented Cube into Certain Trees and Windmill Graphs

The technique used in studying the computational capabilities of interconnection networks and task distribution is graph embedding. Based on the recursively constructed graphs, the hypercube network is popular for its structure. Many variants of hypercube are considered in the literature. Augmented cube is considered as one of the best variants of hypercube as it holds many desirable properties like optimal routing in linear time complexity, vertex symmetricity, wide diameter and maximum connectivity. Our work deals with the exact wirelength, when augmented cube is embedded into certain tree and windmill structures.

Total and paired domination numbers of windmill graphs

Let [Formula: see text] be a graph without isolated vertices. A total dominating set of [Formula: see text] is a set [Formula: see text] of vertices of [Formula: see text] such that every vertex of [Formula: see text] is adjacent to at least one vertex in [Formula: see text]. A total dominating set [Formula: see text] is a paired dominating set of [Formula: see text] if the subgraph of [Formula: see text] induced by [Formula: see text] has a perfect matching. The minimum cardinality of a total dominating set (respectively, a paired dominating set) is called the total domination number (respectively, the paired domination number). This paper determines the total domination numbers and the paired domination numbers of windmill graphs.

English

English

Spektrum Laplace pada graf kincir angin berarah (Q_k^3)

Suppose that 0 = µ0 ≤ µ1 ≤ ... ≤ µn-1 are eigen values of a Laplacian matrix graph with n vertices and m(µ0), m(µ1), …, m(µn-1) are the multiplicity of each µ, so the Laplacian spectrum of a graph can be expressed as a matrix 2 × n whose line elements are µ0, µ1, …, µn-1 for the first row, and m(µ0), m(µ1), …, m(µn-1) for the second row. In this paper, we will discuss Laplacian spectrum of the directed windmill graph () with k ≥ 1. The determination of the Laplacian spectrum in this study is to determine the characteristic polynomial of the Laplacian matrix from the directed windmill graph () with k ≥ 1.
 Keywords: Characteristic polynomial, directed windmill graph, Laplacian matrix, Laplacian spectrum.MSC2020 :05C50

Certain topological indices of Basava wheel windmill graph

In this paper, we have proposed new windmill graph, that is Basava wheel windmill graph. The Basava wheel windmill graph \(W^{(m)}_{n+1}\) is the graph obtained by taking \(m\geq 2\) copies of the graph \(K_1+W_{n}\) for \(n\geq 4\) with a vertex \(K_1\) in common. Inspired by recent work on topological indices, proposed new degree-based topological indices namely, general \(SK_{\alpha}\) and \(SK^{\alpha}_1\) indices of a graph \(G\). We have obtained first and second Zagreb index, F-index, first and second hyper-Zagreb index, harmonic index, Randi\(\acute{c}\) index, general Randi\(\acute{c}\) index, sum connectivity index, general sum connectivity index, atom-bond connectivity index, geometric-arithmetic index, Symmetric division deg index, Sombor index, SK indices, general \(SK_{\alpha}\) and \(SK^{\alpha}_1\) indices of Basava wheel windmill graph. Further, we have computed exact values of these topological indices of chloroquine, hydroxychloroquine and remdesiver.

Windmill Graph based Feature Descriptors for Facial Expression Recognition

Automatic Facial Expression Recognition (FER) is an important research area in computer vision because it has many real-time applications. However, the main issue lies in the design of a feature descriptor that could effectively capture the appearance changes in the facial images. For FER systems, graph based methods have not been much explored for feature extraction. Hence, this paper introduces novel graph based methods named Windmill Graph based Feature Descriptors (WGFD) for feature extraction. Two variants of WGFD’s (WGFDh and WGFDv) have been proposed in this work to effectively encode the relationship among neighboring pixels in a local neighborhood. For expression classification, multi-class Support Vector Machine (SVM) is utilized. The performance of the proposed feature descriptors have been evaluated on six benchmark FER datasets namely JAFFE, KDEF, MUG, CK+, TFEID and FERG with respect to seven expressions classification. The experimental results showed promising results when compared to the recent FER methods.

Group inverses of matrices associated with certain graph classes

We obtain formulae for group inverses of matrices that are associated with a new class of digraphs obtained from stars. This new class contains both bipartite and non-bipartite graphs. Expressions for the group inverse of matrices corresponding to double star digraphs and the adjacency matrix of certain undirected multi-star graphs are also proven. A blockwise representation of the inverse or group inverse of the adjacency matrix of the Dutch windmill graph is presented.

Computing topological indices of certain windmill graphs

Let V (G), be the vertex set of graph G, we define Vd = {v ∈ V (G) : SG(u) = d} in which SG(u) = ∑v∈NG(u) dG(v) and NG(u) = {v ∈ V(G) : uv ∈ E(G)}. In this paper we express the explicit formula for Sanskruti index S(G), fth M1 and M2 Zagreb indices, fifth M1 and M2 multiplicative Zagreb indices for Dutch windmill graph, Kulli cyclic windmill graph, Kulli path windmill graph and French windmill graph.

The Local Antimagic Total Chromatic Number of Some Wheel-Related Graphs

Let G=(V,E) be a connected graph with |V|=n and |E|=m. A bijection f:V(G)∪E(G)→{1,2,⋯,n+m} is called local antimagic total labeling if, for any two adjacent vertices u and v, ωt(u)≠ωt(v), where ωt(u)=f(u)+∑e∈E(u)f(e), and E(u) is the set of edges incident to u. Thus, any local antimagic total labeling induces a proper coloring of G, where the vertex x in G is assigned the color ωt(x). The local antimagic total chromatic number, denoted by χlat(G), is the minimum number of colors taken over all colorings induced by local antimagic total labelings of G. In this paper, we present the local antimagic total chromatic numbers of some wheel-related graphs, such as the fan graph Fn, the bowknot graph Bn,n, the Dutch windmill graph D4n, the analogous Dutch graph AD4n and the flower graph Fn.

Spectral determination of graphs with one positive anti-adjacency eigenvalue

The anti-adjacency matrix (or eccentricity matrix) of a graph is obtained from its distance matrix by retaining for each row and each column only the largest distances. This matrix can be viewed as the opposite of the adjacency matrix, which is, on the contrary, obtained from the distance matrix of a graph by keeping for each row and each column only the distances being 1. In this paper, we prove that the graphs with exactly one positive anti-adjacency eigenvalue are determined by the anti-adjacency spectra. As corollaries, the well-known (generalized) friendship graphs and windmill graphs are shown to be determined by their anti-adjacency spectra.