Corona Product Of Graphs Research Articles

Non-Isolated Resolving Sets of Corona Graphs with Some Regular Graphs

Let G be a connected, simple, and finite graph. For an ordered set W={w1,w2,…,wk}⊆V(G) and a vertex v of G, the representation of v with respect to W is the k-vector r(v|W)=(dG(v,w1),…,dG(v,wk)). The set W is called a resolving set of G, if every two vertices of G has a different representation. A resolving set containing a minimum number of vertices is called a basis of H. The number of elements in a basis of G is called the metric dimension of G and denoted by dim(G). In this paper, we considered a resolving set W of G where the induced subgraph of G by W does not contain an isolated vertex. Such a resolving set is called a non-isolated resolving set. A non-isolated resolving set of G with minimum cardinality is called an nr-set of G. The cardinality of an nr-set of G is called the non-isolated resolving number of G, denoted by nr(G). Let H be a graph. The corona product graph of G with H, denoted by G⊙H, is a graph obtained by taking one copy of G and |V(G)| copies of H, namely H1,H2,…,H|V(G)|, such that the i-th vertex of G is adjacent to every vertex of Hi. If the degree of every vertex of H is k, then H is called a k-regular graph. In this paper, we determined nr(G⊙H) where G is an arbitrary connected graph of order n at least two and H is a k-regular graph of order t with k∈{t−2,t−3}.

HF-Index and Y-Index of Some New Graph of Operations

In this paper we derive HF index of some graph operations containing join, Cartesian Product, Corona Product of graphs and compute the Y index of new operations of graphs related to the join of graphs.

Corona product of signed graphs and its application to modeling signed networks

The notion of corona of two graphs was introduced by Frucht and Harary in 1970. In this paper, we generalize their definition of corona product of two graphs and introduce corona product of two signed graphs by utilizing the framework of marked graphs, which was introduced by Beineke and Harary in 1978. We study structural and spectral properties of corona product of signed graphs. Further, we define signed corona graphs by considering corona product of a fixed small signed graph with itself iteratively, and we call the small graph as the seed graph for the corresponding corona product graphs. Signed corona graphs can be employed as a signed network generative model for large growing signed networks. We study structural properties of corona graphs that include statistics of signed links, all types of signed triangles and degree distribution. Besides we analyze algebraic conflict of signed corona graphs generated by specially structured seed graphs. Finally, we show that a suitable choice of a seed graph can produce corona graphs which preserve properties of real signed networks.

Topological Indices of Families of Bistar and Corona Product of Graphs

Topological indices are graph invariants that are used to correlate the physicochemical properties of a chemical compound with its (molecular) graph. In this study, we study certain degree‐based topological indices such as Randić index, Zagreb indices, multiplicative Zagreb indices, Narumi–Katayama index, atom‐bond connectivity index, augmented Zagreb index, geometric‐arithmetic index, harmonic index, and sum‐connectivity index for the bistar graphs and the corona product , where represents the complement of complete graph Kn.

The Dominant Metric Dimension of Corona Product Graphs

The metric dimension and dominating set are the concept of graph theory that can be developed in terms of the concept and its application in graph operations. One of some concepts in graph theory that combine these two concepts is resolving dominating number. In this paper, the definition of resolving dominating number is presented again as the term dominant metric dimension. The aims of this paper are to find the dominant metric dimension of some special graphs and corona product graphs of the connected graphs and , for some special graphs . The dominant metric dimension of is denoted by and the dominant metric dimension of corona product graph G and H is denoted by .

On independent position sets in graphs

An independent set S of vertices in a graph G is an independent position set if no three vertices of S lie on a common geodesic. An independent position set of maximum size is an ip-set of G. The cardinality of an ip-set is the independent position number, denoted by ip(G). In this paper, we introduce and study the independent position number of a graph. Certain general properties of these concepts are discussed. Graphs of order n having the independent position number 1 or n − 1 are characterized. Bounds for the independent position number of Cartesian and Lexicographic product graphs are determined and the exact value for Corona product graphs are obtained. Finally, some realization results are proved to show that there is no general relationship between independent position sets and other related graph invariants.

The vertex coloring of local antimagic total labeling on corona product graphs

Let G be a graph with the vertex set V(G) and edge set E(G). A function h is a bijective function of domain the union of vertex set and edge set of G and range the natural number {1, 2, 3,… , |V(G)| + |E(G)|. We called the function h as a vertex local antimagic total labeling if for any two adjacent vertices x and x‘, w(x) = w(x’), where w(x) = ∑e∈(x) h(e) + h(x), and E(x) is the set of edges which are incident to x. It is considered to be a proper coloring on vertices of graph G if we assign colour to all vertices with w(x). The minimum number of colors by the vertex local antimagic total labeling of G is called the vertex local antimagic chromatic number, denoted by Xlat(G). We study on the vertex local antimagic total labeling of graphs and determined chromatic number on some corona product graphs, namely corona (G © Cm) where G is isomorphis with path, star, broom, cycle, and sunlet graph.

Structural and spectral properties of the generalized corona networks

In this paper, we present a growing complex network model, namely, the generalized corona network (GCN) which is built on a base network and a sequence of networks by using corona product of graphs. This construction generalizes several existing complex network models. We study the structural properties of the special classes of generalized corona networks and show that these networks have small diameter, the cumulative betweenness distribution follows a power-law distribution, the degree distribution decay exponentially, small average path length with the network order, high clustering coefficient and small-world behavior. Further, we obtain the spectra of the adjacency matrix and the signless Laplacian matrix of GCN when the constituting networks are regular. Also, we obtain the Laplacian spectra for all generalized corona networks. In addition, explicitly give eigenvector corresponding to the adjacency and Laplacian eigenvalues. Finally, we derive the spectral radius and the algebraic connectivity of GCN.

Center Coloring in Graph Operations

Center coloring Cc(G) is a kind of coloring that is to color the vertices of a graph G is such a way that if vertices have different distances from the center then they must receive different colors. Two adjacent vertices can receive the same color. In this paper we observed the behavior of the center coloring under several graph operations such as adding, removing, union, join, sequential join, Cartesian product, corona product of graphs and we get some bounds for center coloring number in these graph operations.

ST-coloring of some products of graphs

For a finite set T of non negative integers containing zero, a function c: V(G) → Z+∪{0} is said to be a ST-coloring of the graph G = (V,E), if |c(x) − c(y)| is not in T for any any edge (x, y) and for any two distinct edges (x, y) and (u, v), |c(x)−c(y)|≠|c(u)−c(v)|. spST (G) is the minimum of the difference between the largest and smallest colors assigned over all the vertices and espST (G) is the minimum of the maximum difference between the colors assigned to the vertices of an edge over all the edges of the graph, where the minimum is taken over all ST-coloring c. Here we establish some results related to ST-chromatic number, span and edge span of some graph products namely, Tensor product, Cartesian product and Corona product of graphs.

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

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

On the edge irregularity strength of corona product of graphs with cycle

Let [Formula: see text] be a simple graph with vertex set [Formula: see text] and edge set [Formula: see text], respectively. An edge irregular [Formula: see text]-labeling of [Formula: see text] is a labeling of [Formula: see text] with labels from the set [Formula: see text] in such a way that for any two different edges [Formula: see text] and [Formula: see text], their weights [Formula: see text] and [Formula: see text] are distinct. The weight of an edge [Formula: see text] in [Formula: see text] is the sum of the labels of the end vertices [Formula: see text] and [Formula: see text]. The minimum [Formula: see text] for which the graph [Formula: see text] has an edge irregular [Formula: see text]-labeling is called the edge irregularity strength of [Formula: see text], denoted by [Formula: see text]. In this paper, we determine the exact value of edge irregularity strength of corona product of graphs with cycle.

Star-rainbow coloring in some corona product graphs

A “rainbow connected graph” is a connected graph in which every pair of distinct vertices in it has a rainbow path, in the sense that no two edges in this path are colored the same. The rainbow connection number of a connected graph G, denoted by rc(G), is the “minimum” number colors necessary to color G such that it has a rainbow path between every pair of its vertices. Further, G is said to be star-rainbow colored if every path on four vertices in it is rainbow colored. The “minimum” number of colors that are necessary to color G such that it is star-rainbow colored is called the “star-rainbow connection number” of G, denoted by strrc(G). In this article, we consider some corona product graphs involving Pn , Kn , Cn and K 1,n and find strrc(G) for such graphs.

Hubungan Dimensi Metrik Ketetanggaan dan Dimensi Metrik Ketetanggan Lokal Graf Hasil Operasi Kali Korona

Adjacency metric dimension and local adjacency metric dimension are the development of metric dimension. The purpose of this research is to determine the adjacency metric dimension of corona graph between any connected graph G and non-trivial graph H denoted by dimA(G⊙H), to determine the local adjacency metric dimension of corona graph between any connected graph G and non-trivial graph H denoted by dimA,l(G⊙H), and to determine the correlation between adjacency metric dimension and local adjacency metric dimension of corona product graph operations. In this research, it is found out that the value of adjacency metric dimension of G⊙H graph is affected by the basic characteristic of H and the domination characteristic. Meanwhile, the value of local adjacency metric dimension of G⊙H graph is only affected by the basic characteristic of H Futhermore, it is found a correlation of adjacency metric dimension and local adjacency metric dimension of corona product graph between any connected graph G and non-trivial graph H.

The upper bound of vertex local antimagic edge labeling on graph operations

Let G(V(G), E(G)) be a connected simple graph and let u, v be two vertices of graph G. A bijective function f from the edge set of G to the natural number up to the number of edges in G is called a vertex local antimagic edge labeling if for any two adjacent vertices v and v′, w(v) = w(v′), where , and E(v) is the set of vertices which is incident to v. Thus any vertex local antimagic edge labeling induces a proper vertex coloring of G where the vertex v is assigned with the color w(v). The vertex local antimagic chromatic number χla (G) is the minimum number of colors taken over all coloring induced by vertex local antimagic edge labeling of G. In this paper, we study the vertex local antimagic edge labeling of graphs and determine the upper bound of vertex local antimagic chromatic number on graph operation, namely cartesian product of graphs, corona product of graphs, and power graph.

The locating dominating set (LDS) of generalized of corona product of path graph and any graphs

Graph G is usually written by G = (V, E) is graph G where V(G) is vertex set on graph G and E(G) is edge set on graph G. Graph G used in this study is only on simple and undirected graphs. Dominating set (DS) is graph G which have a vertex set D, where each vertex in D can dominate the neighboring vertices, in other words every vertex from u ∈ V(G) − D is adjacent to verted v ∈ D. The minimum cardinality of dominating set is called by domination number, symbolized by γ(G). Locating dominating set (LDS) is dominating set with additional condition. A graph G = (V, E) is said to be locating dominating set if the set of vertex dominator D satisfies every vertex that is not D, that is V − D has a different intersection set with D. The minimum cardinality of locating dominating set is called by locating domination number, symbolized by γL (G). In this paper we will determine the LDS on edge corona product. The edge corona product of graph is development of corona product graph. The edge corona of two graphs G and H is obtained by taking one copy of G and |E(G)| copies of H and joining each end vertices of i-th edge of G to every vertex in the i-th copy of H, symbolized by G ⋄ H. The results in this study are shown that there is a relation between the locating dominating set on the basic graph and its operation.

Dimensi Metrik Kuat Lokal Graf Hasil Operasi Kali Kartesian

The strong local metric dimension is the development result of a strong metric dimension study, one of the study topics in graph theory. Some of graphs that have been discovered about strong local metric dimension are path graph, star graph, complete graph, cycle graphs, and the result corona product graph. In the previous study have been built about strong local metric dimensions of corona product graph. The purpose of this research is to determine the strong local metric dimension of cartesian product graph between any connected graph G and H, denoted by dimsl (G x H). In this research, local metric dimension of G x H is influenced by local strong metric dimension of graph G and local strong metric dimension of graph H. Graph G and graph H has at least two order.

Inverse sum indeg coindex of graphs

The inverse sum indeg coindex $\overline{ISI}(G)$ of a simple connected graph $G$ is defined as the sum of the terms $\frac{d_G(u)d_G(v)}{d_G(u)+d_G(v)}$ over all edges $uv$ not in $G,$ where $d_G(u)$ denotes the degree of a vertex $u$ of $G.$ In this paper, we present the upper bounds on inverse sum indeg coindex of edge corona product graph and Mycielskian graph. In addition, we obtain the exact value of both inverse sum indeg index and its coindex of a double graph.

Spectra, Hitting Times and Resistance Distances ofq- Subdivision Graphs

AbstractSubdivision, triangulation, Kronecker product, corona product and many other graph operations or products play an important role in complex networks. In this paper, we study the properties of $q$-subdivision graphs, which have been applied to model complex networks. For a simple connected graph $G$, its $q$-subdivision graph $S_q(G)$ is obtained from $G$ through replacing every edge $uv$ in $G$ by $q$ disjoint paths of length 2, with each path having $u$ and $v$ as its ends. We derive explicit formulas for many quantities of $S_q(G)$ in terms of those corresponding to $G$, including the eigenvalues and eigenvectors of normalized adjacency matrix, two-node hitting time, Kemeny constant, two-node resistance distance, Kirchhoff index, additive degree-Kirchhoff index and multiplicative degree-Kirchhoff index. We also study the properties of the iterated $q$-subdivision graphs, based on which we obtain the closed-form expressions for a family of hierarchical lattices, which has been used to describe scale-free fractal networks.

English

English