Edge connectivity and super edge-connectivity of jump graphs
Xing Chen, Juan Liu, Dongyang Xie, Jixiang Meng · Journal of Information and Optimization Sciences · 2016
For a graph G, let and L(G) denote the complement graph and the line graph of G, and let denote the jump graph of G. It is well-known that κ (G) ≤ λ(G) ≤ δ (G). A graph G is called maximally edge connected if G has edge connectivity of its minimum degree and is called super-(edge-)connected if for every minimum vertex(edge) cut S of G, G – S has isolated vertices. In this paper, we apply previous results of edge-connectivity and super-connectivity and super-edge-connectivity to give the following four results on jump graphs: (1) Characterization of the graph G having ω(J (G)) = 2; (2) If J(G) is connected, then J(G) is maximally edge connected; (3) Characterization of the graph G whose J(G) is super edge connected but not super-connected; (4) Give a sufficient condition for J(G) is super edge connected.