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 * of a graph is that graph whose vertex set is and in which two vertices are adjacent if and only if they are adjacent or incident in . 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.

**[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