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 | References | Similar Articles | Additional Information
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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- Mehdi Behzad and Heydar Radjavi, The total group of a graph, Proc. Amer. Math. Soc. 19 (1968), 158–163. MR 218271, DOI https://doi.org/10.1090/S0002-9939-1968-0218271-5
- Mehdi Behzad and Heydar Radjavi, Structure of regular total graphs, J. London Math. Soc. 44 (1969), 433–436. MR 236046, DOI https://doi.org/10.1112/jlms/s1-44.1.433
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Additional Information
Keywords:
Total graphs
Article copyright:
© Copyright 1970
American Mathematical Society