Dependence of Graph Energy on Nullity: A Case Study

作者：Gutman Ivan^*; Triantafillo Irene

来源：MATCH-Communications in Mathematical and in Computer Chemistry, 2016, 76(3): 761-769.

The nullity n(0) of a graph G is the algebraic multiplicity of the number zero in the spectrum of G. The energy epsilon of G is the sum of absolute values of the eigenvalues of G. A long-open problem in the theory of graph energy is the relation between epsilon and no, i.e., the dependence of epsilon on n(0). Arguments from quantum chemistry suggest that epsilon should be a decreasing function of n(0) , but no mathematical verification of this conjecture is known. We now offer a case study, in which the validity of the conjecture is confirmed within a special class of graphs called banana trees.

• 出版日期2016