Path connectivity of line graphs

2016/03/13 by Yaping Mao, Mao, Yaping · 3 citations
Computer Science · Materials Science · Mathematics · #Advanced Graph Theory Research #Graphene research and applications #Interconnection Networks and Systems #math.CO

paper · pdf · doi:10.48550/arxiv.1603.03995

15 pages. arXiv admin note: substantial text overlap with arXiv:1508.07202, arXiv:1207.1838; text overlap with arXiv:1103.6095 by other authors

arxiv created 2016/03/13 · arxiv updated 2016/03/15

Abstract

Dirac showed that in a (k-1)-connected graph there is a path through each k vertices. The path k-connectivity π_k(G) of a graph G, which is a generalization of Dirac's notion, was introduced by Hager in 1986. In this paper, we study path connectivity of line graphs.

Citations

• Constructing Internally Disjoint Pendant Steiner Trees in Cartesian Product Networks
• A survey on the generalized connectivity of graphs
• The generalized 3-connectivity of Cartesian product graphs

Cited by

• Pendant-tree connectivity of line graphs
• The minimal size of graphs with given pendant-tree connectivity
• The generalized 3-(edge) connectivity of total graphs

Related

• Pendant-tree connectivity of line graphs
• On a property of 2-connected graphs and Dirac's Theorem
• A Dirac-type Characterization of k-chordal Graphs
• Connectivity keeping paths in k-connected bipartite graphs
• A Common Generalization of Dirac's two Theorems