<abstract xmlns="http://www.w3.org/1999/xhtml"> For a graph G with vertex set V(G) = {v1, v2, . . . , vn}, the extended double cover G* is a bipartite graph with bipartition (X, Y), X = {x1, x2, . . . , xn} and Y = {y1, y2, . . . , yn}, where two vertices xi and yj are adjacent if and only if i = j or vi adjacent to vj in G. The double graph D[G] of G is a graph obtained by taking two copies of G and joining each vertex in one copy with the neighbors of corresponding vertex in another copy. In this paper we study energy and Laplacian energy of the graphs G* and D[G], L-spectra of Gk* the k-th iterated extended double cover of G. We obtain a formula for the number of spanning trees of G*. We also obtain some new families of equienergetic and L-equienergetic graphs.</abstract>

For a graph G with vertex set V(G) = {v1, v2, . . . , vn}, the extended double cover G* is a bipartite graph with bipartition (X, Y), X = {x1, x2, . . . , xn} and Y = {y1, y2, . . . , yn}, where two vertices xi and yj are adjacent if and only if i = j or vi adjacent to vj in G. The double graph D[G] of G is a graph obtained by taking two copies of G and joining each vertex in one copy with the neighbors of corresponding vertex in another copy. In this paper we study energy and Laplacian energy of the graphs G* and D[G], L-spectra of Gk* the k-th iterated extended double cover of G. We obtain a formula for the number of spanning trees of G*. We also obtain some new families of equienergetic and L-equienergetic graphs.

Energy, Laplacian energy of double graphs and new families of equienergetic graphs

Eötvös Loránd University Faculty of Informatics Budapest

Acta Universitatis Sapientiae, Informatica

This article is distributed under the terms of the Creative Commons Attribution Non-Commercial License, which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

For a graph G with vertex set V(G) = {v1, v2, . . . , vn}, the extended double cover G* is a bipartite graph with bipartition (X, Y), X = {x1, x2, . . . , xn}...

Energy, Laplacian energy of double graphs and new families of equienergetic graphs

Published Online: Jun 27, 2014

Page range: 89 - 116

Received: Feb 03, 2014

DOI: https://doi.org/10.2478/ausi-2014-0020

Keywords
double graph, spectra, energy, Laplacian energy, L-equienergetic, equienergetic

© 2014

This article is distributed under the terms of the Creative Commons Attribution Non-Commercial License, which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

Energy, Laplacian energy of double graphs and new families of equienergetic graphs

Published Online: Jun 27, 2014

Page range: 89 - 116

Received: Feb 03, 2014

DOI: https://doi.org/10.2478/ausi-2014-0020

Keywordsdouble graph, spectra, energy, Laplacian energy, L-equienergetic, equienergetic

© 2014

This article is distributed under the terms of the Creative Commons Attribution Non-Commercial License, which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

Keywords
double graph, spectra, energy, Laplacian energy, L-equienergetic, equienergetic