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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A characterization of total graphs

Author: M. Behzad
Journal: Proc. Amer. Math. Soc. 26 (1970), 383-389
MSC: Primary 05.40
MathSciNet review: 0266786
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Abstract: We consider ``ordinary'' graphs; that is, finite undirected graphs with no loops or multiple edges. The total graph $ T(G)$ of a graph $ G$ is that graph whose vertex set is $ V(G) \cup E(G)$ and in which two vertices are adjacent if and only if they are adjacent or incident in $ 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.

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Keywords: Total graphs
Article copyright: © Copyright 1970 American Mathematical Society

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