A note on Bartholdi zeta function and graph invariants based on resistance distance

作者：Li, Deqiong; Hou, Yaoping^*

来源：Discrete Mathematics, 2018, 341(3): 786-792.

DOI：10.1016/j.disc.2017.11.018

• Bartholdi zeta function
• Resistance distance
• Complexity
• Kirchhoff index

Let G be a finite connected graph. In this note, we show that the complexity of G can be obtained from the partial derivatives at (1 - 1/t, t) of a determinant in terms of the Bartholdi zeta function of G. Moreover, the second order partial derivatives at (1 - 1/t, t) of this determinant can all be expressed as the linear combination of the Kirchhoff index, the additive degree-Kirchhoff index, and the multiplicative degree-Kirchhoff index of the graph G.

• 出版日期2018-3
• 单位湖南师范大学; 湖南科技大学