A Performance on Harmonious Coloring of Barbell Graph
M.S. Franklin Thamil Selvi1, A. Amutha2

1M.S. Franklin Thamil Selvi*, Deparment of Mathematics, Sathyabama Institute of Science and Technology, Chennai, India.
2A. Amutha, Department of Mathematics, The American College, Madurai, India.
Manuscript received on September 22, 2019. | Revised Manuscript received on October 20, 2019. | Manuscript published on October 30, 2019. | PP: 1583-1586 | Volume-9 Issue-1, October 2019 | Retrieval Number: A2625109119/2019©BEIESP | DOI: 10.35940/ijeat.A2625.109119
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© The Authors. 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: Given simple graph 𝑮, a harmonious chromatic number 𝝌𝒉(𝑮) is the minimum number of colors used in a graph such that no two adjacent vertices receives the same color and each combination of color seems together on atmost one edge. In this article we have determined the harmonious chromatic number of barbell and central graph of barbell graph. Over all we have given an algorithm to calculate the harmonious chromatic number of Barbell graph by depicting a quadratic time.
Keywords: Harmonious coloring, Barbell graph, Central graph.