Degree resistance distance of trees with some given parameters

Document Type: Research Paper


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


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.


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