Study of Total Graph Using Dynamic Graph Operation

Abstract

"Auxiliary graphs are graphs which are used to translate one graph problem to another graph problem. Total graph is also an auxiliary graph which is used to translate the total coloring problem into the vertex coloring problem. Dynamic graph operation on a graph is defined as sequence of update operation on the graph, where update operations are add vertex/edge and remove edge/vertex. This thesis derives some new characteristics of total graph. By using existing properties and new properties, we have developed algorithms to find maximal total sub graph of an arbitrary nontotal graph. We have devised a procedure by using which we are able tomigrate set of edges form vertex-vertex part to edgevertex part, together with some allied operations such that the resulting graph is also a total graph. For super total graph we have provided some characteristics which is required to add a vertex/edge."