A connected graph is highly irregular if each of its vertices is adjacent only to vertices with distinct degrees. In this paper w e investigate several problems concerning the existence and enumeration of highly irregular graphs as well as their independence numbers, with particular focus on the cor
Highly irregular digraphs
β Scribed by Yousef Alavi; Jiuqiang Liu; Jianfang Wang
- Publisher
- Elsevier Science
- Year
- 1993
- Tongue
- English
- Weight
- 406 KB
- Volume
- 111
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
β¦ Synopsis
A connected digraph D is highly irregular if the vertices of out-neighborhood of each vertex UE V(D) have different out-degrees. In this paper, we investigate some problems concerning the existence of highly irregular digraphs with special properties, with particular focus on highly irregular directed trees as well as their independence numbers.
π SIMILAR VOLUMES
A graph is highly irregular if it is connected and the neighbors of each vertex have distinct degrees. In this paper, we study existence and extremal problems for highly irregular graphs with a given maximum degree and focus our attention on highly irregular graphs that are m-chromatic for m 3 2.
The main purpose of this note is to construct an infinite , highly arc-transitive digraph with finite out-valency , and with out-spread greater than 1 , which does not have the two-way infinite path Z as a homomorphic image . This answers Question 3 . 8 in the paper [3] of Cameron , Praeger and Worm