A characterization of total graphs

Behzad, M.

doi:10.1090/S0002-9939-1970-0266786-5

A characterization of total graphs

Author: M. Behzad
Journal: Proc. Amer. Math. Soc. 26 (1970), 383-389
MSC: Primary 05.40
DOI: https://doi.org/10.1090/S0002-9939-1970-0266786-5
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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