Degree Distance in Graphs with Forbidden Subgraphs

Abstract

Let G be a simple, connected graph with minimum degree δ ≥ 2, order n, diameter diam(G) = d and degree distance D ′ (G).We prove thatAlthough no construction has been found to show that the bounds are asymptotically tight, apart from improving known results in the literature, for triangle-free graphs the results confirm that an upper bound on the degree distance 1 32 n 4 +O(n 3 ) conjectured by Dobrynin and Kochetova holds.This in conjunction with an infinite family of triangle-free graphs we construct in this paper that attain an upper bound on the degree distance, 1 8 nd n -1 2 δd 2 + O(n 3 ), give a guide for further research.