General Pattern of Total Coloring of a Prism Graph of 𝑛-Layers and a Grid Graph
S. Sudha1, K. Manikandan2
1Dr. S. Sudha, Professor of Mathematics, Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chennai, India.
2K. Manikandan, Research scholar, Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chennai, India.
Manuscript received on February 01, 2015. | Revised Manuscript received on February 09, 2015. | Manuscript published on February 15, 2015. | PP: 33-37 | Volume-3 Issue-3, February 2015. | Retrieval Number: C0809023315/2015©BEIESP
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© The Authors. Published By: Blue Eyes Intelligence Engineering and Sciences Publication (BEIESP). This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Abstract: Behzad [1] introduced the total coloring of a graph 𝑮 as an assignment of colors to the elements (vertices and edges) of 𝑮 such that no two elements receive the same color. In this paper, we have obtained the total coloring of prism graph of 𝒏-layers and grid graphs in general using five colors only and found that the total-chromatic number is ∆(𝑮) + 𝟏 = 𝟓 for both prism graph of 𝒏-layers and grid graphs. AMS Subject Classification: 05C15
Keywords: Total coloring, prism graph of 𝒏-layers, grid graphs.