The connectivity of line-graphs
β Scribed by Gary Chartrand; M. James Stewart
- Publisher
- Springer
- Year
- 1969
- Tongue
- English
- Weight
- 286 KB
- Volume
- 182
- Category
- Article
- ISSN
- 0025-5831
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
## Abstract Chartrand and Stewart have shown that the line graph of an __n__βconnected graph is itself __n__βconnected. This paper shows that for every pair of integers __m__ > __n__ > 1 there is a graph of point connectivity __n__ whose line graph has point connectivity __m__. The corresponding qu
## Abstract Let __G__ be a graph and let __V__~0~β=β{Ξ½β __V__(__G__): __d__~__G__~(Ξ½)β=β6}. We show in this paper that: (i) if __G__ is a 6βconnected line graph and if |__V__~0~|ββ€β29 or __G__[__V__~0~] contains at most 5 vertex disjoint __K__~4~'s, then __G__ is Hamiltonβconnected; (ii) every 8βco
A well-known conjecture of Thomassen says that every 4-connected line graph is hamiltonian. In this paper we prove that every 7-connected line graph is hamiltonian-connected. For line graph, C. Thomassen [l] made the following conjecture. Conjecture. Every 4-connected line graph is hamiltonian.
## Abstract Sharp lower bounds for the point connectivity and line connectivity of the line graph __L(G__) and the total graph __T(G__) of a graph __G__ are determined. The lower bounds are expressed in terms of the point connectivity __k__, line connectivity Ξ», and minimum degree Ξ΄ of __G.__ It is