A NOVEL APPROACH FOR COLORING OF FUZZY GRAPH

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A NOVEL APPROACH FOR COLORING OF FUZZY GRAPH

Ganesh Kumar Thakur

¹

,Bandana Priya

²

1Assistant Professor,Krishna Engineering College,Ghaziabad

2Associate Professor,G L Bajaj Institute of Technology & management

Graph theory has various applications but sometimes it provides uncertain solutions and hence in order to overcome this, fuzzy graph theory is adopted. Fuzzy graph for any application will be processed by applying the concept of graph coloring because it is one of the most vital concepts in graph theory and it is exploited in many real time applications like scheduling, network security, map coloring, and Global System for Mobile (GSM) mobile phone networks, and so forth .Given a graph G=(V,E), a coloring function C assigns an integer value C(i) to each node i∈V in such a way that the extremes of any edge {i,j}∈E cannot share the same color, i.e., C(i)≠C(j). A new approaches to the graph coloring problem of a fuzzy graph are introduced in this paper. The classical concept of the (crisp) chromatic number of a graph is generalized for this approaches.. The approach is based on an extension of the concept of coloring function by means of a distance defined between colors. A new algorithm for obtaining the chromatic number associated with the second approach is proposed.

Keywords : Fuzzy graph,Coloring of Graph,Coloring of Fuzzy Graph