All Connected Graphs with Maximum Degree at Most 3 whose Energies are Equal to the Number of Vertices

作者：Li, Xueliang^*; Ma, Hongping

来源：MATCH-Communications in Mathematical and in Computer Chemistry, 2010, 64(1): 7-24.

The energy E(G) of a graph G is defined as the sum of the absolute values of its eigenvalues. Let S(2) be the star of order 2 (or K(2)) and Q be the graph obtained from S(2) by attaching two pendent edges, to each of the end vertices of S(2). Majstorovic et al. conjectured that S(2), Q and the complete bipartite graphs K(2,2) and K(3,3) are the only connected graphs with maximum degree Delta <= 3 whose energies are equal to the number of vertices. This paper is devoted to giving a confirmative proof to this conjecture.

• 出版日期2010
• 单位南开大学