A Comparative Study on Acyclic Vertex Coloring Graph of Monochromatic and Bi-chromatic |
Author(s): |
| R. Radhamani , Vivekanandha College for Women; R. Akila, Assistant Professor, Department of Mathematics, Vivekanandha College for Women; A. Niranjana , Assistant Professor, Department of Mathematics, Vivekanandha College for Women; G. Sathishkumar, Assistant Professor, Department of Mathematics, Vivekanandha College for Women; L. Yogeswari, Assistant Professor, Department of Mathematics, Vivekanandha College of Arts and Sciences for Women |
Keywords: |
| Acyclic Vertex Coloring Graph, Monochromatic, Bi-Chromatic |
Abstract |
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An acyclic vertex coloring of a graph which adjacent vertices are allowed to have the same color, as long as the monochromatic components induced by the corresponding edges have a certain structure. Due to its important applications, as for example in the binarization of graphs, this type of coloring has been extensively studied, mainly with respect to the size, degree, and acyclicity of the monochromatic components. An acyclic vertex coloring of a graph is a proper vertex coloring such that there are no bichromatic cycles. The acyclic chromatic number of G, denoted a(G), is the minimum number of colors required for acyclic vertex coloring of graph G = (V,E).In this paper In this paper, we show that any graph G with maximum degree Δ can be acyclically colored using C(Δ) colors. |
Other Details |
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Paper ID: IJSRDV6I90112 Published in: Volume : 6, Issue : 9 Publication Date: 01/12/2018 Page(s): 235-239 |
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