Star-in-Coloring of Arbitrary Super Subdivision of Graphs and the Splitting Graphs
S. Sudha1, V. Kanniga2
1Dr. S. Sudha, Professor of Mathematics, Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chennai, India.
2V. Kanniga, Ph.D Research Scholar, Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chennai, India.
Manuscript received on March 03, 2015. | Revised Manuscript received on March 09, 2015. | Manuscript published on March 15, 2015. | PP: 13-21 | Volume-3 Issue-4, March 2015. | Retrieval Number: D0813033415/2015©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: In this paper, we have shown that the arbitrary supersubdivision of a path, a cycle, a fan graph, a wheel graph, a helm graph and a gear graph by a complete bi-partite graph K2,m for any m admits star-in-coloring. In addition, we have proved the fan graph and the splitting graph of a path, a cycle and a fan graph also admit star-in-coloring. 2000 Mathematics Subject Classification: 05C15, 05C20.
Keywords: Star-in-coloring, splitting graph, fan graph, wheel graph, helm graph, gear graph.