On Some Graph Operations and Related Applications

Yegnanarayanan, V.; Thiripurasundari, P.R.; Padmavathy, T. V.

doi:10.1016/j.endm.2009.03.018

Cited by 15 publications

(9 citation statements)

References 8 publications

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“…The hypercube Q n is one of the most versatile, efficient, and popular topological structures of interconnection networks. Q n has many excellent features, so it becomes the first choice for the topological structure of computing systems and parallel processing [8,20]. The topological structure of hypercube Q n is included in the lexicographic graph P 2 P 2 P 2 · · · P 2 n , n 2.…”

Section: Corollary 1 ([12]mentioning

confidence: 99%

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The number of spanning trees in a new lexicographic product of graphs

Liang

Zhao

2014

Sci. China Inf. Sci.

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The problem of counting the number of spanning trees is an old topic in graph theory with important applications to reliable network design. Usually, it is desirable to put forward a formula of the number of spanning trees for various graphs, which is not only interesting in its own right but also in practice. Since some large graphs can be composed of some existing smaller graphs by using the product of graphs, the number of spanning trees of such large graph is also closely related to that of the corresponding smaller ones. In this article, we establish a formula for the number of spanning trees in the lexicographic product of two graphs, in which one graph is an arbitrary graph G and the other is a complete multipartite graph. The results extend some of the previous work, which is closely related to the number of vertices and Lapalacian eigenvalues of smaller graphs only.

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Section: Corollary 1 ([12]mentioning

confidence: 99%

“…There will be an edge between (u 1 , u 2 ) and (v 1 , v 2 ) if an edge connecting u 1 and v 1 exists in G 1 , or if u 1 = v 1 and then an edge connecting u 2 and v 2 exists in G 2 . Sometimes, the lexicographic product is called the composition or the wreath product [17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

The number of spanning trees in a new lexicographic product of graphs

Liang

Zhao

2014

Sci. China Inf. Sci.

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“…Graph operations, especially graph products, play a significant role not only in pure and applied mathematics but also in computer science, chemistry, electrical engineering, and pharmaceutics. For instance, the Cartesian product provides a significant model for connecting computers [12].…”

Section: Introductionmentioning

confidence: 99%

Three Topological Indices of Two New Variants of Graph Products

Bilal

Jamil

Waheed

et al. 2021

Mathematical Problems in Engineering

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Graph operations play an important role to constructing complex network structures from simple graphs, and these complex networks play vital roles in different fields such as computer science, chemistry, and social sciences. Computation of topological indices of these complex network structures via graph operation is an important task. In this study, we defined two new variants of graph products, namely, corona join and subdivision vertex join products and investigated exact expressions of the first and second Zagreb indices and first reformulated Zagreb index for these new products.

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“…Mathematic structures can be properly understood if one has a grasp of their symmetries; it also helps to know whether they can be constructed from smaller constituents, since many large graphs (networks) are usually composed from some existing smaller graphs (networks) through graph operations (say, product [10]). In this paper, we are mainly concerned with the number of spanning trees of the composition of two graphs.…”

Section: Introductionmentioning

confidence: 99%

The Number of Spanning Trees in the Composition Graphs

2014

Mathematical Problems in Engineering

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Using the composition of some existing smaller graphs to construct some large graphs, the number of spanning trees and the Laplacian eigenvalues of such large graphs are also closely related to those of the corresponding smaller ones. By using tools from linear algebra and matrix theory, we establish closed formulae for the number of spanning trees of the composition of two graphs with one of them being an arbitrary complete 3-partite graph and the other being an arbitrary graph. Our results extend some of the previous work, which depend on the structural parameters such as the number of vertices and eigenvalues of the small graphs only.

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On Some Graph Operations and Related Applications

Cited by 15 publications

References 8 publications

The number of spanning trees in a new lexicographic product of graphs

The number of spanning trees in a new lexicographic product of graphs

Three Topological Indices of Two New Variants of Graph Products

The Number of Spanning Trees in the Composition Graphs

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