On the construction of L -equienergetic graphs

摘要

For a graph G with n vertices and m edges, and having Laplacian spectrum μ 1 , μ 2 , … , μ n and signless Laplacian spectrum μ 1 + , μ 2 + , … , μ n + , the Laplacian energy and signless Laplacian energy of G are respectively, defined as L E ( G ) = ∑ i = 1 n | μ i ? 2 m n | and L E + ( G ) = ∑ i = 1 n | μ i + ? 2 m n | . Two graphs G 1 and G 2 of same order are said to be L -equienergetic if L E ( G 1 ) = L E ( G 2 ) and Q -equienergetic if L E + ( G 1 ) = L E + ( G 2 ) . 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.