A criterion for (non-)planarity of the transformation graphGxyzwhenxyz= – + +

Basavanagoud, A.; Patil, Prashant V.

doi:10.1080/09720529.2010.10698318

Cited by 6 publications

(3 citation statements)

References 3 publications

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“…if and only if q and q ′ are either incident or linked in Q. e total graphs of paths P n and cycle C 6 are shown in Figure 1. Some characteristics of total graphs are described in the literature [24][25][26][27][28][29].…”

Section: Introductionmentioning

confidence: 99%

Properties of Total Transformation Graphs for General Sum-Connectivity Index

et al. 2021

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The study of networks and graphs through structural properties is a massive area of research with developing significance. One of the methods used in studying structural properties is obtaining quantitative measures that encode structural data of the whole network by the real number. A large collection of numerical descriptors and associated graphs have been used to examine the whole structure of networks. In these analyses, degree-related topological indices have a significant position in theoretical chemistry and nanotechnology. Thus, the computation of degree-related indices is one of the successful topics of research. The general sum-connectivity GSC index of graph Q is described as χ ρ Q = ∑ qq ′ ∈ E Q d q + d q ′ ρ , where d q presents the degree of the vertex q in Q and ρ is a real number. The total graph T Q is a graph whose vertex set is V Q ∪ E Q , and two vertices are linked in T Q if and only if they are either adjacent or incident in Q . In this article, we study the general sum-connectivity index χ ρ Q of total graphs for different values of ρ by using Jensen’s inequality.

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Section: Introductionmentioning

confidence: 99%

Properties of Total Transformation Graphs for General Sum-Connectivity Index

et al. 2021

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“…For example, the Zagreb indices of transformation graphs and total transformation graphs were calculated by Basavanagoud and Patil [10] and Hosamani and Gutman [11], respectively. Wu and Meng [12] investigated the basic properties (connectedness, graph equations and iteration, and diameter) of total transformation.…”

Section: The Transformation Graphmentioning

confidence: 99%

Sharp Bounds for the General Sum-Connectivity Indices of Transformation Graphs

Wang

Liu

Wang

et al. 2017

Discrete Dynamics in Nature and Society

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Given a graph , the general sum-connectivity index is defined as ( ) = ∑ V∈ ( ) ( ( ) + (V)) , where ( ) (or (V)) denotes the degree of vertex (or V) in the graph and is a real number. In this paper, we obtain the sharp bounds for general sum-connectivity indices of several graph transformations, including the semitotal-point graph, semitotal-line graph, total graph, and eight distinct transformation graphs V , where , V, ∈ {+, −}.

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“…[7]denote the point set, line set of graph G respectively. The Transformation graph G ++- [4,8]of G is the graph with point set V(G) E(G) in which the points X andY are joined by a line if one of the following conditions hold.…”

Section: Introductionmentioning

confidence: 99%