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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.


References [Enhancements On Off] (What's this?)

  • [1] M. Behzad, A criterion for the planarity of the total graph of a graph, Proc. Cambridge Philos. Soc. 63 (1967), 679-681. MR 35 #2771. MR 0211896 (35:2771)
  • [2] -, The connectivity of total graphs, Australian Math. Bull. 1 (1969), 175-181. MR 0262096 (41:6706)
  • [3] -, The total chromatic number of a graph: A survey, Proc. Conference Combinatorial Mathematics (Oxford, England, 1969), Academic Press, New York, 1970.
  • [4] M. Behzad and G. Chartrand, Total graphs and traversability, Proc. Edinburgh Math. Soc. (2) 15 (1966/67), 117-120. MR 36 #1351. MR 0218264 (36:1351)
  • [5] -, An introduction to theory of graphs, Allyn and Bacon, Boston, Mass. (to appear). MR 0432461 (55:5449)
  • [6] M. Behzad and H. Radjavi, The total group of a graph, Proc. Amer. Math. Soc. 19 (1968), 158-163. MR 36 #1358. MR 0218271 (36:1358)
  • [7] -, Structure of regular total graphs, J. London Math. Soc. 44 (1969), 433-436. MR 38 #4344. MR 0236046 (38:4344)
  • [8] F. Harary, Graph theory, Addison-Wesley, Reading, Mass., 1969. MR 0256911 (41:1566)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1970-0266786-5
Keywords: Total graphs
Article copyright: © Copyright 1970 American Mathematical Society

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