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)={u, v\} ⊆ V (G)(d_G (u)+ d_G (v))\, d (u, v), where d G (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.
D'(G)={u, v\} ⊆ V (G)(d_G (u)+ d_G (v))\, d (u, v), where d G (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.
Abstract
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 d G (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.
Springer
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