Degree Distance of Unicyclic Graphs with Given Matching Number

Let G be a connected graph with vertex set V(G). The degree distance of G is defined as $${D'(G) = \sum_{\{u, v\}\subseteq V(G)} (d_G(u) + d_G (v))\, d(u,v)}$$, where dG (u) is the degree of vertex u, d(u, v) denotes the distance between u and v, and the summation goes over all pairs of vertices in G. In this paper, we characterize n-vertex unicyclic graphs with given matching number and minimal degree distance.

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