Median Eigenvalues of Bipartite Planar Graphs

作者：Mohar Bojan^*

来源：MATCH-Communications in Mathematical and in Computer Chemistry, 2013, 70(1): 79-84.

Motivated by the problem about HOMO-LUMO separation that arises in mathematical chemistry, Fowler and Pisanski [2, 3] introduced the notion of the HL-index which measures how large in absolute value may be the median eigenvalues of a graph. In this note we prove that the median eigenvalues of every bipartite planar graph of maximum degree at most three belong to the interval [-1, 1]. This proves the bipartite case of a conjecture of the author that was proposed in [6].

• 出版日期2013