On the eccentric distance sum of unicyclic graphs with a given matching number

Abstract

Let $G=(V_G,E_G)$ be a simple connected graph. The eccentric distance sum of $G$ is defined as ${\xi }^d(G)={\sum }_{v\in V_G}{\epsilon }_G(v)D_G(v),$ where ${\epsilon }_G(v)$ is the eccentricity of the vertex $v$ and $D_G(v)={\sum }_{u\in V_G}d(u,v)$ is the sum of all distances from the vertex $v$. In this paper, we characterize $n$-vertex unicyclic graphs with given matching number having the minimal and second minimal eccentric distance sums, respectively.

14 pages, 1 figure