ON GENERALIZED k-DIAMETER OF k-REGULAR k-CONNECTED GRAPHS

Abstract

In this paper, motivated by the study of the wide diameter and the Rabin number of graphs, we define the generalized $k$-diameter of $k$-connected graphs, and show that every $k$-regular $k$-connected graph on $n$ vertices has the generalized $k$-diameter at most $n/2$ and this upper bound cannot be improved when $n=4k-6+i(2k-4)$.