A characterization of total graphs-Reference-Cited by-同舟云学术

A characterization of total graphs

Published:1970 Issue:3 Volume:26 Page:383-389
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Behzad M.

Abstract

We consider “ordinary” graphs; that is, finite undirected graphs with no loops or multiple edges. The total graph T ( G ) T(G) of a graph G G is that graph whose vertex set is V ( G ) ∪ E ( G ) V(G) \cup E(G) and in which two vertices are adjacent if and only if they are adjacent or incident in G G . A characterization of regular total graphs as well as some other properties of total graphs have been considered before. In this article we consider nonregular graphs and yield a method which enables us actually to determine whether or not they are total.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1970-026-03/S0002-9939-1970-0266786-5/S0002-9939-1970-0266786-5.pdf

Reference8 articles.

1. A criterion for the planarity of the total graph of a graph;Behzad, Mehdi;Proc. Cambridge Philos. Soc.,1967

2. The connectivity of total graphs;Behzad, Mehdi;Bull. Austral. Math. Soc.,1969

3. \bysame, The total chromatic number of a graph: A survey, Proc. Conference Combinatorial Mathematics (Oxford, England, 1969), Academic Press, New York, 1970.

4. Total graphs and traversability;Behzad, Mehdi;Proc. Edinburgh Math. Soc. (2),1966

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