Proof of conjectures on remoteness and proximity in graphs
β Scribed by Hua, Hongbo; Das, Kinkar Ch.
- Book ID
- 121690916
- Publisher
- Elsevier Science
- Year
- 2014
- Tongue
- English
- Weight
- 340 KB
- Volume
- 171
- Category
- Article
- ISSN
- 0166-218X
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π SIMILAR VOLUMES
The transmission of a vertex in a connected graph is the sum of all distances from that vertex to the others. It is said to be normalized if divided by n -1, where n denotes the order of the graph. The proximity of a graph is the minimum normalized transmission, while the remoteness is the maximum n
Let G = (V, E) be a graph and N G [v] the closed neighborhood of a vertex v in G. For k β N, the minimum cardinality of a set In this note we prove the following conjecture of Rautenbach and Volkmann [D. Rautenbach, L. Volkmann, New bounds on the k-domination number and the k-tuple domination numbe
## Abstract Let __ir__(__G__) and Ξ³(__G__) be the irredundance number and the domination number of a graph __G__, respectively. A graph __G__ is called __irredundance perfect__ if __ir__(__H__)=Ξ³(__H__), for every induced subgraph __H__ of __G__. In this article we present a result which immediatel
It was conjectured in [Wang, to appear in The Australasian Journal of Combinatorics] that, for each integer k β₯ 2, there exists . This conjecture is also verified for k = 2, 3 in [Wang, to appear; Wang, manuscript]. In this article, we prove this conjecture to be true if n β₯ 3k, i.e., M (k) β€ 3k. W