𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Highly irregular graphs

✍ Scribed by Yousef Alavi; Gary Chartrand; F. R. K. Chung; Paul Erdös; R. L. Graham; Ortrud R. Oellermann

Publisher
John Wiley and Sons
Year
1987
Tongue
English
Weight
531 KB
Volume
11
Category
Article
ISSN
0364-9024

No coin nor oath required. For personal study only.

✦ Synopsis

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 corresponding problems for highly irregular trees.

📜 SIMILAR VOLUMES

Highly irregular m-chromatic graphs
Highly irregular m-chromatic graphs
✍ Yousef Alavi; Fred Buckley; Marc Shamula; Sergio Ruiz 📂 Article 📅 1988 🏛 Elsevier Science 🌐 English ⚖ 620 KB

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.

Highly irregular graphs with extreme num
Highly irregular graphs with extreme numbers of edges
✍ Zofia Majcher; Jerzy Michael 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 219 KB

A simple connected graph is highly irregular if each of its vertices is adjacent only to vertices with distinct degrees. In this paper we find: (1) the greatest number of edges of a highly irregular graph with n vertices, where n is an odd integer (for n even this number is given in [1]), (2) the sm

Highly irregular digraphs
Highly irregular digraphs
✍ Yousef Alavi; Jiuqiang Liu; Jianfang Wang 📂 Article 📅 1993 🏛 Elsevier Science 🌐 English ⚖ 406 KB

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 direct

On graph irregularity strength
On graph irregularity strength
✍ Alan Frieze; Ronald J. Gould; Michał Karoński; Florian Pfender 📂 Article 📅 2002 🏛 John Wiley and Sons 🌐 English ⚖ 132 KB

## Abstract An assignment of positive integer weights to the edges of a simple graph __G__ is called irregular, if the weighted degrees of the vertices are all different. The irregularity strength, __s__(__G__), is the maximal weight, minimized over all irregular assignments. In this study, we show