He, F., Jiang, X. (2018). Degree resistance distance of trees with some given parameters. Transactions on Combinatorics, 7(4), 11-24. doi: 10.22108/toc.2018.108656.1538

Fangguo He; Xinnong Jiang. "Degree resistance distance of trees with some given parameters". Transactions on Combinatorics, 7, 4, 2018, 11-24. doi: 10.22108/toc.2018.108656.1538

He, F., Jiang, X. (2018). 'Degree resistance distance of trees with some given parameters', Transactions on Combinatorics, 7(4), pp. 11-24. doi: 10.22108/toc.2018.108656.1538

He, F., Jiang, X. Degree resistance distance of trees with some given parameters. Transactions on Combinatorics, 2018; 7(4): 11-24. doi: 10.22108/toc.2018.108656.1538

Degree resistance distance of trees with some given parameters

^{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.