Study A Degree Sum Condition With Connectivity For Relative Length of Shortest Paths and Cycles


Arockia Jancy K
Dept. of Mathematics, Auxilium College of arts and science, Rugunathapuram, Tamil Nadu


A graph G, p(G) denote the orders of a Shortest Path c(G) and denote the orders of a shortest cycle in G. For a graph G, we denote by dG(y) and k(G) the degree of a vertex y in G respectively. In this paper we prove that if G is a 2-connected graph of order n such that ∑3j=1 dG (yi) ≥ n + k(G) + 2 for every independent set {y1, y2, y3}, then p(G) - c(G) ≤ 1.

October 19, 2023