On the construction of L-equienergetic graphs

Abstract

For a graph G with n vertices and m edges, and having Laplacian spectrum μ1,μ2,…,μn and signless Laplacian spectrum μ1+,μ2+,…,μn+, the Laplacian energy and signless Laplacian energy of G are respectively, defined as LE(G)=∑i=1n|μi−2mn| and LE+(G)=∑i=1n|μi+−2mn|. Two graphs G1 and G2 of same order are said to be L-equienergetic if LE(G1)=LE(G2) and Q-equienergetic if LE+(G1)=LE+(G2). The problem of constructing graphs having same Laplacian energy was considered by Stevanovic for threshold graphs and by Liu and Liu for those graphs whose order is n≡0 (mod 7). We consider the problem of constructing L-equienergetic graphs from any pair of given graphs and we construct sequences of non-cospectral (Laplacian, signless Laplacian) L-equienergetic and Q-equienergetic graphs from any pair of graphs having same number of vertices and edges.

Keywords

• Laplacian energy
• Spectra
• Signless Laplacian energy
• L-equienergetic
• Q-equienergetic