A Study on b-Chromatic Number with Product Graphs

Abstract

A brief introduction accord about the origin of graph theory, graph coloring and its newlineapplications has been discussed. It deals with basic and fundamental definitions of graph theory newlineand graph coloring which are used for constructing the graphs relating to the study. The bchromatic newlinenumber of vertex corona product of path graph with origami graph, origami graph with newlinepath graph, cycle graph with origami graph, origami graph with cycle graph , bistar graph with newlinepath graph, path graph with bistar graph, bistar graph with cycle graph ,cycle graph with bistar newlinegraph are obtained . The b-chromatic number of vertex corona product of tadpole graph with path newlinegraph, tadpole graph with cycle graph, path graph with tadpole graph, barbell graph with cycle newlinegraph and barbell graph with path graph are derived. The b-chromatic number newlineand#61531;C B(K , K )and#61533; n n n and#61546; and#61551; for n and#61619; 3, [ C ° T ] n 4,n and#61546; for n and#61501; 3,n and#61501; 4,n and#61619; 5 , [ C ° F ] n 1,n and#61546; for n and#61501; 3,n and#61619; 4 and newline[ C ° F ] n 2,n and#61546; for n and#61501; 3,n and#61619; 4 are derived. The b-chromatic number of vertex corona product of double newlinefan graph with cycle graph, fan graph with star graph, fan graph with wheel graph, double fan newlinegraph with path graph, path graph with barbell graph are obtained. Algorithmic approach is used newlineto find some results. The exact value for the b-chromatic number of vertex corona product of star newlinegraph with fan graph, wheel graph with fan graph, fan graph with cycle graph, fan graph with path newlinegraph, path graph with fan graph and fan graph with double fan graph are derived. Provides an newlineintroduction, idea and the need for vehicular ad hoc networks. The proposed CLAT algorithm is newlinecompared to Chinese remainder theorem (CRT) in various parameters like alert message newlinedissemination, pocket delivery ratio, number of nodes vs energy consumption in joules. newlinei) Major objectives : newlineand#61623; To evaluate b-chromatic number of corona product of some graphs using Vertex newlinecorona method and b-coloring method. newlineand#61623; To apply CLAT method for alert message dissemination in vanet using vertex newlinecoloring