Constructing pairs of equienergetic and non-cospectral graphs

Bonifácio, Andréa Soares; Vinagre, Cybele T. M.; Abreu, Nair Maria Maia de

doi:10.1016/j.aml.2007.04.002

Cited by 29 publications

(17 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Cospectral sidigraphs are obviously equienergetic, therefore problem of equienergetic sidigraphs reduces to problem of construction of noncospectral pairs of equinergetic sidigraphs such that for every pair not both sidigraphs are cycle balanced. The problem of construction of equienergetic sigraphs is an open problem [7] and for equienergetic graphs see [4,19]. Theorem 6.1.…”

Section: Equienergetic Sidigraphsmentioning

confidence: 99%

Energy of signed digraphs

Pirzada

Bhat

2014

Discrete Applied Mathematics

View full text Add to dashboard Cite

In this paper we extend the concept of energy to signed digraphs. We obtain Coulson's integral formula for energy of signed digraphs. Formulae for energies of signed directed cycles are computed and it is shown that energy of non cycle balanced signed directed cycles increases monotonically with respect to number of vertices. Characterization of signed digraphs having energy equal to zero is given. We extend the concept of non complete extended p sum (or briefly, NEPS) to signed digraphs. An infinite family of equienergetic signed digraphs is constructed. Moreover, we extend McClelland's inequality to signed digraphs and also obtain sharp upper bound for energy of signed digraph in terms the number of arcs. Some open problems are also given at the end.2010 Mathematics Subject Classification. 05C50, 05C22,05C76.

show abstract

Section: Equienergetic Sidigraphsmentioning

confidence: 99%

Energy of signed digraphs

Pirzada

Bhat

2014

Discrete Applied Mathematics

View full text Add to dashboard Cite

show abstract

“…In [22] and [31], the authors calculated the energy of unitary Cayley graphs and complement of unitary Cayley graphs, and establish the necessary and sufficient conditions for ICG n to be hyperenergetic. There was a vast research for the pairs and families of non-cospectral graphs having equal energy [10,11,24,25,27,28,30,36].…”

Section: Introductionmentioning

confidence: 99%

New results on the energy of integral circulant graphs

Ilić

Bašić

2011

Applied Mathematics and Computation

View full text Add to dashboard Cite

Circulant graphs are an important class of interconnection networks in parallel and distributed computing. Integral circulant graphs play an important role in modeling quantum spin networks supporting the perfect state transfer as well. The integral circulant graph ICG n (D) has the vertex set Z n = {0, 1, 2, . . . , n − 1} and vertices a and b are adjacent if gcd(a − b, n) ∈ D, where D ⊆ {d : d | n, 1 ≤ d < n}. These graphs are highly symmetric, have integral spectra and some remarkable properties connecting chemical graph theory and number theory. The energy of a graph was first defined by Gutman, as the sum of the absolute values of the eigenvalues of the adjacency matrix. Recently, there was a vast research for the pairs and families of non-cospectral graphs having equal energies. Following [R. B. Bapat, S. Pati, Energy of a graph is never an odd integer, Bull. Kerala Math. Assoc. 1 (2004) 129-132.], we characterize the energy of integral circulant graph modulo 4. Furthermore, we establish some general closed form expressions for the energy of integral circulant graphs and generalize some results from [A. Ilić, The energy of unitary Cayley graphs, Linear Algebra Appl. 431 (2009), 1881-1889.]. We close the paper by proposing some open problems and characterizing extremal graphs with minimal energy among integral circulant graphs with n vertices, provided n is even.

show abstract

“…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

View full text Add to dashboard Cite

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.

show abstract

Constructing pairs of equienergetic and non-cospectral graphs

Cited by 29 publications

References 4 publications

Energy of signed digraphs

Energy of signed digraphs

New results on the energy of integral circulant graphs

Seidel Equienergetic Graphs

Contact Info

Product

Resources

About