A Study On BColoring Of Graphs With A Metric Relationship To Achromatic Star Equitable And Harmonious Colorings

Abstract

newlineA graph is a collection of vertices and edges often represented by points newlineand connecting lines in the plane A proper coloring of the graph assigns colors to newlinethe vertices edges or both so that proximal elements are assigned distinct colors newlineConcepts and questions of graph coloring arise naturally from practical problems newlineand have found applications in many areas including Information Theory and most newlinenotably Theoretical Computer Science This thesis discusses about bcoloring and newlineits relationship with few other types of colorings newlineA bcoloring of a graph G is a proper coloring of the vertices of G such that newlinethere exists a vertex in each color class joined to at least one vertex in each other newlinecolor class The bchromatic number of a graph G denoted by G is the maximal newlineinteger k such that G may have a bcoloring with k colors newlineIn this thesis the author investigated the bchromatic number of middle newlinetotal and line graph of some families of graphs and also found the corona of any newlinetwo graphs and presented the bchromatic number of central graph middle graph newlineand total graph of star graph and discussed the relationship between bchromatic newlinenumber with some other types of chromatic numbers such as achromatic number newlinestar chromatic number and equitable chromatic number newlineThe author has also obtained the bchromatic number for the central graph newlinemiddle graph total graph and line graph of double star graph and has found a metric newlinerelationship between the bchromatic number and three other coloring parameters newlinethe equitable chromatic number harmonious chromatic number and the achromatic newlinenumber The author has also discussed the harmonious chromatic number of the newlinecorona product of any graph G of order with the complete graph K for newlineAs a consequence of this work the author also obtains the harmonious chromatic newlinenumber of t copies of K for t n 1 Also it is conjectured that the bchromatic newlinenumber is bounded by the harmonious chromatic number newline newline newline newline newline newline newline newline newline newline newline newline newline newline newline newline newline