A note on the LEL-equienergetic graphs

作者：Liu, Muhuo; Liu, Bolian^*

来源：Ars Combinatoria, 2014, 113: 435-439.

• LAPLACIAN-ENERGY

Let G be a graph with n vertices and mu(1), mu(2),..., mu(n) be the Laplacian eigenvalues of G. The Laplacian-energy-like graph invariant LEL(G) = Sigma(n)(i=1) root mu i, has been defined and investigated in [1]. Two non-isomorphic-graphs G(1) and G(2) of the same order are said to be LEL-equienergetic if LEL (G(1)) = LE L(G(2)). In [2], three pairs of LEL-equienergetic non-cospectral connected graphs are given. It is also claimed([2]) that the LEL-equienergetic non-cospectral connected graphs are relatively rare. It is natural to consider the question: Whether the number of the LEL-equienergetic non-cospectral connected graphs is finite? The answer is negative, because we shall construct a pair of LEL-equienergetic non-cospectral connected graphs of order n, for all n >= 12 in this paper.

• 出版日期2014-1
• 单位华南师范大学; 华南农业大学; 南京师范大学