Graphs with large generalized (edge-)connectivity

2013/05/06 by Xueliang Li, Li, Xueliang, Yaping Mao +1
Mathematics · #05C05 #05C40 #05C70 #05C75 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05C05 #msc:05C40 #msc:05C70 #msc:05C75

paper · pdf · doi:10.48550/arxiv.1305.1089

25 pages. arXiv admin note: text overlap with arXiv:1207.1838

arxiv created 2015/08/31 · arxiv updated 2015/09/01

Abstract

The generalized k-connectivity κ_k(G) of a graph G, introduced by Hager in 1985, is a nice generalization of the classical connectivity. Recently, as a natural counterpart, we proposed the concept of generalized k-edge-connectivity λ_k(G). In this paper, graphs of order n such that κ_k(G)=n-(k)/(2)-1 and λ_k(G)=n-(k)/(2)-1 for even k are characterized.

Citations

• A survey on the generalized connectivity of graphs

Related

• A survey on the generalized connectivity of graphs
• On the generalized (edge-)connectivity of graphs
• Further hardness results on the generalized connectivity of graphs
• The generalized 3-(edge) connectivity of total graphs
• Extremality and Sharp Bounds for the k-edge-connectivity of Graphs