Hilal A. Ganie

Spectra, Energy and Laplacian Energy of Strong Double Graphs

For a graph G with vertex set \(V (G)\,=\,\{v_{1},v_{2},\cdots \,,v_{n}\}\), the strong double graph SD(G) is a graph obtained by taking two copies of G and joining each vertex v i in one copy with the closed neighbourhood N[v i ] = N(v i ) ∪{ v i } of corresponding vertex in another copy. In this paper, we study spectra, energy and Laplacian energy of the graph SD(G). We also obtain some new families of equienergetic and L-equienergetic graphs, and an infinite family of graphs G for which LE(G) < E(G). We derive a formula for the number of spanning trees of SD(G) in terms of the number of spanning trees of G.

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

On energy, Laplacian energy and

For a graph

p

G

-fold graphs

having adjacency spectrum (

On the bounds for signless Laplacian energy of a graph

A

Properties of Strong Double Graphs

-spectrum)

Comparison between Laplacian--energy--like invariant and Kirchhoff index

\lambda_n\leq\lambda_{n-1}\leq\cdots\leq\lambda_1

On the Laplacian eigenvalues of a graph and Laplacian energy

and Laplacian spectrum (

On Laplacian-energy-like invariant and incidence energy

L