Abstract
The graph obtained by the famous Mycielski’s construction is called the Mycielski graph. This paper focuses on the relation between the basic graphs and two classes of constructed graphs on the (adjacent) vertex-distinguishing total coloring. And some sufficient conditions with which the Mycielski graphs and the Cartesian product graphs satisfy the adjacent vertex-distinguishing total coloring conjecture are given.
Supported by the National Natural Science Council(10471078).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bollobas, B.: Modern Graph Theory. Springer, Berlin Heidelberg New York (1998)
Chartrand, G., Lesniak-Foster, L.: Graph and Digraphs, Ind. Edition. Wadsworth Brooks/Cole, Monterey (1986)
Reinhard, D.: Graph Theory. Springer, Berlin Heidelberg New York (1997)
Hansen, P., Marcotte, O.: Graph Coloring and Application. AMS providence, Rhode Island USA (1999)
Bondy, J.A., Murty, U.S.R.: Graph Theory with Applications. North-Holland (1976)
Mycielski, J.: Sur Le Coloring des Graphes. Colloq. Math. 3, 161–162 (1955)
Čižek, N., Klavžar, S.: On the Chromatic Number of the Lexicographic Product and the Cartesian Sum of Graphs. Discrete Math. 134, 17–24 (1994)
Klavžar, S.: Coloring Graph Products—A Survey. Diserete Math. 155, 135–145 (1996)
Zhang, Z.F., Li, J.W., Chen, J.W., et al.: On The Vertex-Distinguish Total Coloring of Graphs. Science Report of Northwest Normal University, vol 168 (2003)
Zhang, Z.F., Liu, L.Z., Wang, J.F.: Adjacent Strong Edge Coloring of Graphs. Applied Math. Letters 15, 623–626 (2002)
Zhang, Z.F., Li, J.W., Chen, X.E., et al.:D(β)-Vertex-distinguishing Total Coloring of Graphs. Science in China (to appear)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer Berlin Heidelberg
About this paper
Cite this paper
Sun, Y., Sun, L. (2007). The (Adjacent) Vertex-Distinguishing Total Coloring of the Mycielski Graphs and the Cartesian Product Graphs. In: Akiyama, J., Chen, W.Y.C., Kano, M., Li, X., Yu, Q. (eds) Discrete Geometry, Combinatorics and Graph Theory. CJCDGCGT 2005. Lecture Notes in Computer Science, vol 4381. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70666-3_21
Download citation
DOI: https://doi.org/10.1007/978-3-540-70666-3_21
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-70665-6
Online ISBN: 978-3-540-70666-3
eBook Packages: Computer ScienceComputer Science (R0)