Corona Product Of Graphs Research Articles

On Study of Some Bounds for Fault-Tolerant Metric Dimension and Adjacency Fault-Tolerant Resolving Set of Corona Product Graphs

On Study of Some Bounds for Fault-Tolerant Metric Dimension and Adjacency Fault-Tolerant Resolving Set of Corona Product Graphs

Metric Dimension of Corona Product and Join Graph of Zero Divisor Graphs of Direct Product of Finite Fields

The metric dimension of a graph is the smallest number of vertices such that all vertices are uniquely determined by their distances to the chosen vertices. The corona product of graphs G and H is the graph G ⊙ H obtained by taking one copy of G , called the center graph, | V ( G ) | copies of H , called the outer graph, and making the j t h vertex of G adjacent to every vertex of the j t h copy of H , where 1 ⩽ j ⩽ | V ( G ) | . The Join graph G + H of two graphs G and H is the graph with vertex set V ( G + H ) = V ( G ) ∪ V ( H ) and edge set E ( G + H ) = E ( G ) ∪ E ( H ) ∪ { u v : u ∈ V ( G ) , v ∈ V ( H ) } . In this paper, we determine the Metric dimension of Corona product and Join graph of zero divisor graphs of direct product of finite fields.

A Study of Families of Bistar and Corona Product of Graph: Reverse Topological Indices

In the field of cheminformatics, the amalgamation of graph theory, chemistry, along with technology facilitates the establishment of connections between the structural as well as physiochemical attributes of organic compounds by employing certain valuable graph invariants including the corresponding molecular graph. In this work, we examine reverse topological indices, for instance, the reverse Zagreb index, the reverse arithmetic-geometric, the geometric-arithmetic, the reverse Nirmala indices for the bistar graphs B(n;m) , the reverse sum-connectivity index, the reverse Sombor as well as the corona product of Km∘K′n.

Monophonic graphoidal covering number of corona product graphs

In a graph G, a chordless path is called a monophonic path. A collection ψm of monophonic paths in G is called a monophonic graphoidal cover of G if every vertex of G is an internal vertex of at most one monophonic path in ψm and every edge of G is in exactly one monophonic path in ψm. The monophonic graphoidal covering number ηm(G) of G is the minimum cardinality of a monophonic graphoidal cover of G. In this paper, we find the monophonic graphoidal covering number of corona product of some standard graphs.

Mapping Connectivity Patterns: Degree-Based Topological Indices of Corona Product Graphs

Graph theory (GT) is a mathematical field that involves the study of graphs or diagrams that contain points and lines to represent the representation of mathematical truth in a diagrammatic format. From simple graphs, complex network architectures can be built using graph operations. Topological indices (TI) are graph invariants that correlate the physicochemical and interesting properties of different graphs. TI deal with many properties of molecular structure as well. It is important to compute the TI of complex structures. The corona product (CP) of two graphs G and H gives us a new graph obtained by taking one copy of G and V G copies of H and joining the i th vertex of G to every vertex in the i th copy of H . In this paper, based on various CP graphs composed of paths, cycles, and complete graphs, the geometric index (GA) and atom bond connectivity (ABC) index are investigated. Particularly, we discussed the corona products P s ⨀ P t , C t ⨀ C s , K t ⊙ K s , K t ⊙ P s , and P s ⊙ K t and GA and ABC index. Moreover, a few molecular graphs and physicochemical features may be predicted by considering relevant mathematical findings supported by proofs.

On local distance antimagic labeling of graphs

Let G = ( V , E ) be a graph of order n and let f : V → { 1 , 2 … , n } be a bijection. For every vertex v ∈ V , we define the weight of the vertex v as w ( v ) = ∑ x ∈ N ( v ) f ( x ) where N(v) is the open neighborhood of the vertex v. The bijection f is said to be a local distance antimagic labeling of G if w ( u ) ≠ w ( v ) for every pair of adjacent vertices u , v ∈ V . The local distance antimagic labeling f defines a proper vertex coloring of the graph G, where the vertex v is assigned the color w(v). We define the local distance antimagic chromatic number χ l d ( G ) to be the minimum number of colors taken over all colorings induced by local distance antimagic labelings of G. In this paper we obtain the local distance antimagic labelings for several families of graphs including the path Pn , the cycle Cn , the wheel graph Wn , friendship graph Fn , the corona product of graphs G ° K m ¯ , complete multipartite graph and some special types of the caterpillars. We also find upper bounds for the local distance antimagic chromatic number for these families of graphs.

SUM CORDIAL LABELING OF CORONA PRODUCT GRAPH OF PATH TO PATH

In this paper the researcher studies on the labeling of Corona Product Graph of Path to Path by admitting the certain condition of Sum cordial labeling. A sum cordial labeling of a graph is a binary labeling with vertex set V, with edge labeling f:E(G) {0,1},defined by f(uv)=(f(u)+f(v))(mod2) if |vf(0)-vf(1)|≤1and |ef(0)-ef(1)|≤1. A graph G is Sum cordial if it admits Sum cordial labeling.

S-coindex of some graph operations and its properties and conjugated polymers

The theory of chemical graphs is a field of mathematical chemistry that applies graph theory to the mathematical modeling of chemical phenomena. Topological index is a numerical descriptor of a molecule; it is found that there is strong correlation between the properties of chemical compounds and their molecular structure based on a specific topological feature of the corresponding molecular graph. The S-index of a graph is defined as the sum of five of the degree of vertices of a graph. In this paper, we introduce a new invariant of a graph which is identified as S-coindex. We study some basic mathematical properties and different types of graph operations like as Join, Cartesian Product, Composition, Tensor Product, Strong Product, Disjunction, Symmetric Difference, Corona Product of graphs.

Computing Y-index of Different Corona Products of Graphs

The Y-index of a graph is defined by the sum of four of degrees of the vertices of a graph. Among the all topological indices the Zagreb indices have been used more considerably than any other topological indices in chemical literature. The concept of Corona Product is a recent inclusion to mathematical vocabulary. One of the most significant graph operations is the corona product of several generic and specific graphs, which is one of the most well-known graph products. In this study, we derive some explicit formulations of several corona product types, including subdivision-vertex corona, subdivision-edge corona, subdivision-vertex neighborhood corona, subdivision-edge neighborhood corona, and vertex-edge corona of two graphs.

Correction to: Hitting Times of Random Walks on Edge Corona Product Graphs

Correction to: Hitting Times of Random Walks on Edge Corona Product Graphs

Proper d-Lucky Labeling of Corona Products of Certain Graphs

Objectives: The objective of this paper is to find exact proper d-lucky number for corona product graphs of certain graphs. Methods: The results are proved by method of elaboration and construction. Findings: Exact proper d-lucky numbers are obtained for corona products: Pn⊙ Cm, Pn⊙ Km,Cn⊙ Kn and Kn⊙ Kn. Novelty: Proper d-lucky labeling for the corona product of Pn⊙Cm, Pn⊙ Km, Cn⊙ Kn and Kn⊙ Kn are not studied by any other authors, thus the proper dlucky numbers for the above graphs are new findings. Keywords: Lucky labeling; Proper labeling; d-lucky labeling; Proper d-lucky labeling; Corona product

Total distance vertex irregularity strength of some corona product graphs

A distance vertex irregular total k -labeling of a simple undirected graph G = G ( V , E ) , is a function f : V ( G )∪ E ( G )→{1, 2, …, k } such that for every pair vertices u , v ∈ V ( G ) and u ≠ v , the weights of u and v are distinct. The weight of vertex v ∈ V ( G ) is defined to be the sum of the label of vertices in neighborhood of v and the label of all incident edges to v . The total distance vertex irregularity strength of G (denoted by t d i s ( G ) ) is the minimum of k for which G has a distance vertex irregular total k -labeling. In this paper, we present several results of the total distance vertex irregularity strength of some corona product graphs.

A note on fold thickness of graphs

A 1-fold of G is the graph G0 obtained from a graph G by identifying two nonadjacent vertices in G having at least one common neighbor and reducing the resulting multiple edges to simple edges. A uniform k-folding of a graph G is a sequence of graphs G = G0, G1, G2,...,Gk, where Gi+1 is a 1-fold of Gi for i = 0, 1, 2,...,k − 1 such that all graphs in the sequence are singular or all of them are nonsingular. The largest k for which there exists a uniform k- folding of G is called fold thickness of G and this concept was first introduced in [1]. In this paper, we determine fold thickness of corona product graph G ʘ Km , G ʘ S Km , and graph join G + Km .

The sum of hamming distance for some composite graphs relative to vertex-edge incidence matrix

Given C be a vertex-edge incidence matrix of a graph Z. The Hamming distance between two rows C(x, :) and C(y, :) of C is the number of coloumn ℓ such that C (x, ℓ) ≠ C (y, ℓ). In this paper, we discuss the sum of Hamming distances between all pairs of rows of C. We present a formula for the sum of the number of edges and the number of vertices of the graph Z. We then use this formula to determine the sum of Hamming distance for composite graphs such as union of graphs, joint of graphs, corona product of graphs and cartesian product of graphs

The doubly metric dimension of corona product graphs

The doubly metric dimension of a connected graph G is the minimum cardinality of doubly resolving sets in it. It is well known that deciding the doubly metric dimension of G is NP-complete. The corona product G ? H of two vertex-disjoint graphs G and H is defined as the graph obtained from G and H by taking one copy of G and |V(G)| copies of H, then joining the ith vertex of G to every vertex in the ith copy of H. In this paper some formulae on the doubly metric dimension of corona product G?H of graphs G and H are established in terms of the order of G with the adjacency dimension of H and the doubly metric dimension of K1 ? H, respectively. We determine both sharp upper and lower bounds on doubly metric dimension of corona product graphs with disconnected and connected coronas involved, respectively, and characterize the corresponding extremal graphs. We also characterize all graphs G of diameter two with doubly metric dimension two. Furthermore, the exact values are obtained for the doubly metric dimensions of corona product graphs, being the corona either a path or a cycle.

Proper d-Lucky Labeling of Rooted Products and Corona Products of Certain Graphs

Objectives: To examine rooted products graph and corona product of path graph with itself and cycle graph with itself for the existence of d-lucky labeling. Methods: In this study, d-lucky number for Rooted product graph of path graph to path graph (Pn ◦ Pn) and Corona product graph (Pn⊙ Pn) are computed. Method of construction is used throughout this paper to prove the theorems. Findings: Rooted products and corona products of path with itself and cycle graph with itself admit d-lucky labeling and d-lucky numbers for the same are obtained. Novelty: d-lucky numbers for some graphs are obtained by some authors but for rooted product of path with itself and corona products of path with itself and cycle with itself are new findings. Keywords: Proper Lucky labeling; Rooted product; corona product; d-lucky; d-lucky labeling

A Note on Outer-Independent 2-Rainbow Domination in Graphs

Let G be a graph with vertex set V(G) and f:V(G)→{∅,{1},{2},{1,2}} be a function. We say that f is an outer-independent 2-rainbow dominating function on G if the following two conditions hold: (i)V∅={x∈V(G):f(x)=∅} is an independent set of G. (ii)∪u∈N(v)f(u)={1,2} for every vertex v∈V∅. The outer-independent 2-rainbow domination number of G, denoted by γr2oi(G), is the minimum weight ω(f)=∑x∈V(G)|f(x)| among all outer-independent 2-rainbow dominating functions f on G. In this note, we obtain new results on the previous domination parameter. Some of our results are tight bounds which improve the well-known bounds β(G)≤γr2oi(G)≤2β(G), where β(G) denotes the vertex cover number of G. Finally, we study the outer-independent 2-rainbow domination number of the join, lexicographic, and corona product graphs. In particular, we show that, for these three product graphs, the parameter achieves equality in the lower bound of the previous inequality chain.

On Some New Signed Unidomination Parameters of Corona Product Graph of a Wheel with a Star

On Some New Signed Unidomination Parameters of Corona Product Graph of a Wheel with a Star

Antimagic Labeling for Product of Regular Graphs

An antimagic labeling of a graph G=(V,E) is a bijection from the set of edges of G to 1,2,⋯,E(G) and such that any two vertices of G have distinct vertex sums where the vertex sum of a vertex v in V(G) is nothing but the sum of all the incident edge labeling of G. In this paper, we discussed the antimagicness of rooted product and corona product of graphs. We proved that if we let G be a connected t-regular graph and H be a connected k-regular graph, then the rooted product of graph G and H admits antimagic labeling if t≥k. Moreover, we proved that if we let G be a connected t-regular graph and H be a connected k-regular graph, then the corona product of graph G and H admits antimagic labeling for all t,k≥2.

Structures devised by the generalizations of two graph operations and their topological descriptors

Abstract Graph theory served in different fields of sciences, especially in chemistry in which creating complex structures and studying their enormous properties. Graph operation is a tool to construct complex chemical structures using basic graphs. While studying their properties, topological descriptors are a well-known methodology introduced by chemists, and even after half of a century past, it is still serving. Formally, a topological descriptor or index is a numerical value corresponding to a chemical structure. This numerical value can be easily accessed by a particular equation, for example, the second Zagreb index, the first reformulated Zagreb, and also from the forgotten topological descriptor. In this particular work, we generalized two existing graph operations, and by using these newly developed graph operations, we created two complex structures by using two graph operations, namely, the corona product and double graph operation. Furthermore, to evaluate the chemical properties of these newly generated structures, we used the methodology of topological descriptors, particularly the first and second Zagreb, the first reformulated Zagreb, and forgotten topological descriptors. Moreover, we also presented the closed formulas of the first and second Zagreb co-indices for these newly generated structures.