The generalized 3-edge-connectivity of lexicographic product graphs

Abstract

The generalized $k$-edge-connectivity ${\lambda }_k(G)$ of a graph $G$ is a generalization of the concept of edge-connectivity. The lexicographic product of two graphs $G$ and $H$, denoted by $G\circ H$, is an important graph product. In this paper, we mainly study the generalized 3-edge-connectivity of $G\circ H$, and get upper and lower bounds of ${\lambda }_3(G\circ H)$. Moreover, all bounds are sharp.

14 pages