On the (n, m)-graphs with minimum degree resistance distance

Abstract

The resistance distance r(u, v) between two vertices u, v of a connected graph G is defined as the effective resistance between them in the corresponding electrical network, constructed from g by replacing each edge of g with a unit resistor. The degree resistance distance of g is defined as Dr(g) = σ(u,v)⊆ (d(u) + d(v))r(u,v), where d(u) is the degree of the vertex u. Let Qn,m be the set of connected graphs with order n and m edges. In this paper, we'll determine the extremal graphs among Qn,m with the minimum degree resistance distance.