Degree resistance distance of trees with some given parameters

Document Type: Research Paper

Authors

1 College of Mathematics and Physics, Huanggang Normal University, Huanggang, China

2 College of Life Science and Techonolgy, Huazhong University of Science and Technology, Wuhan

Abstract

The degree resistance distance of a graph $G$ is defined as $D_R(G)=\sum_{i<j}(d(v_i)+d(v_j))R(v_i,v_j)$, where $d(v_i)$ is the degree of the vertex $v_i$, and $R(v_i,v_j)$ is the resistance distance between the vertices $v_i$ and $v_j$. Here we characterize the extremal graphs with respect to degree resistance distance among trees with given diameter, number of pendent vertices, independence number, covering number, and maximum degree, respectively.

Keywords

Main Subjects