Equienergetic net-regular signed graphs

Nayak, Nutan G.

doi:10.12988/ijcms.2014.410108

Cited by 3 publications

(2 citation statements)

References 10 publications

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“…The total degree and net-degree of u are given by d ± (u) = d + (u) + d − (u) and d(u) = d + (u) − d − (u), respectively. A signed graph is called net-regular if every node of it has the same net-degree d [29]. Note that net-regular signed graphs are signed counterpart of unsigned regular graphs.…”

Section: Introductionmentioning

confidence: 99%

Corona product of signed graphs and its application to signed network modelling

Adhikari¹,

Singh²,

Yadav³

2019

Preprint

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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 triads 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.

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Section: Introductionmentioning

confidence: 99%

Corona product of signed graphs and its application to signed network modelling

Adhikari¹,

Singh²,

Yadav³

2019

Preprint

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“…For obvious reason Seidel cospectral graphs are Seidel equienergetic. Several results on equienergetic graphs [2,4,5,15,24,27,28,29,30,31], distance equienergetic graphs [14,23,26], Laplacian equienergetic graphs [8], equienergetic digraphs [17], skew equienergetic digraphs [1,25], equienergetic sigraphs [3,9,10,19] and equienergetic sidigraphs [21] were reported in the literature.…”

Section: Introductionmentioning

confidence: 99%

Seidel Equienergetic Graphs

Ramane

Gundloor

Hosamani³

2016

BMSA

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Abstract. The Seidel matrix S(G) of a graph G is the square matrix with diagonal entries zeroes and off diagonal entries are -1 or 1 corresponding to the adjacency and non-adjacency. The Seidel energy SE(G) of G is defined as the sum of the absolute values of the eigenvalues of S(G). Two graphs G 1 and G 2 are said to be Seidel equienergetic if SE(G 1 ) = SE(G 2 ). We establish an expression for the characteristic polynomial of the Seidel matrix and for the Seidel energy of the join of regular graphs. Thereby construct Seidel non cospectral, Seidel equienergetic graphs on n vertices, for all n ≥ 12.

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On Net-Regular Signed Graphs

Nayak¹

2016

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Equienergetic net-regular signed graphs

Cited by 3 publications

References 10 publications

Corona product of signed graphs and its application to signed network modelling

Corona product of signed graphs and its application to signed network modelling

Seidel Equienergetic Graphs

On Net-Regular Signed Graphs

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