The kdomination number of a graph G, y k ( G ) , is the least cardinality of a set U of verticies such that any other vertex is adjacent to at least k vertices of U. We prove that if each vertex has degree at least k. then YAG) 5 kp/(k + 1).
An Upper Bound for the Total Domination Subdivision Number of a Graph
β Scribed by H. Karami; R. Khoeilar; S. M. Sheikholeslami; A. Khodkar
- Publisher
- Springer Japan
- Year
- 2009
- Tongue
- English
- Weight
- 130 KB
- Volume
- 25
- Category
- Article
- ISSN
- 0911-0119
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
Let G be a simple graph of order n and minimum degree $. The independent domination number i(G) is defined to be the minimum cardinality among all maximal independent sets of vertices of G. In this paper, we show that i(G) n+2$&2 -n$. Thus a conjecture of Favaron is settled in the affirmative.
## Abstract In this paper we consider those graphs that have maximum degree at least 1/__k__ times their order, where __k__ is a (small) positive integer. A result of Hajnal and SzemerΓ©di concerning equitable vertexβcolorings and an adaptation of the standard proof of Vizing's Theorem are used to s