Degree Sums, Connectivity and Dominating Cycles in Graphs
β Scribed by Zhiren Sun; Feng Tian; Bing Wei
- Book ID
- 105749249
- Publisher
- Springer Japan
- Year
- 2001
- Tongue
- English
- Weight
- 124 KB
- Volume
- 17
- Category
- Article
- ISSN
- 0911-0119
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π SIMILAR VOLUMES
## Abstract For a graph __G__, we denote by __d__~__G__~(__x__) and ΞΊ(__G__) the degree of a vertex __x__ in __G__ and the connectivity of __G__, respectively. In this article, we show that if __G__ is a 3βconnected graph of order __n__ such that __d__~__G__~(__x__) + __d__~__G__~(__y__) + __d__~__
Let G be a connected graph of order n, and let NC2(G) denote min{ [N(u) UN(v)[: In this paper, we prove that if G contains a dominating cycle and ~ ~> 2, then G contains a dominating cycle of length at least min{n,2NC2(G)-3}.
A cycle in a graph is dominating if every vertex lies at distance at most one from the cycle and a cycle is D-cycle if every edge is incident with a vertex of the cycle. In this paper, first we provide recursive formulae for finding a shortest dominating cycle in a Hahn graph; minor modifications ca