IllansitionalValues of Graphs

M. A. Johneonintroduceda wayto describea chemicaltransformationby labeling eachvertexandedgeofa graphGwith oneofintegem-1, O,1. The labelingofGsoobtainedis called a transitional labelingof G. The valueof a transitional labelingof G is definedas the minimumof the numberof negativeelementsof G and the numberofpositiveelementsofG. Weintroducea new invariantofa graphG calledthe transitionalvalueofG, definedas the maximumvalueamongall the valueaofthe transitional labelingsofG. This parameterprovideaa meesureofthe structural changea that occurin a chemicaltransformationrepresentwlby a transitionallabelingofG. Wedeterminethe transitional valueaofsomefamilieaofgraphsand characterizethe transitional labelingsof maximum valueof completegraphs. Kq_wmrdS-Mathematical chemistry,Appliedgraphtheory,Labelings,Distancesin graphs.