Connectivity and domination in weighted graph structures

Abstract

Graph theory has moved on with immense pace and has reached new newlineheights in the previous decade by taking contributions from weighted newlinegraphs, which plays a signiand#57346;cant role in various and#57346;elds like interconnection newlinenetworks, information theory, database theory, etc. Connectivity has laid the newlinefoundation for many of these applications of weighted graphs. Domination newlinealso has played its part in converting graph theory into a mainstream subject newlineof applied mathematics. Some related applications also depend upon the newlinedeand#57346;nitions of spanning trees, strong edges, strong cycles and paths, etc. newlineWhen we consider a weighted graph network, the weak edges in it do not newlinecontribute much to the dynamics of network, and hence they can be ignored newlinein most of the situations. We are trying to study diand#57345;erent connectivity and newlineadjacency properties in weighted graph structures with the help of strong newlineedges. Several authors including J.A.Bondy, Genghua Fan, Sunil Mathew newlineand M S Sunitha had put forward various connectivity concepts in weighted newlinegraphs inspired from the spark given by Dirac and Grotschel. newlineIn graphs, a k-container between two vertices is a set of k internally disjoint newlinepaths between them. The connectivity of a graph is related to the number of newlinevertices whose removal leaves the remaining graph disconnected or trivial. newline