• TOTAL EFICIENT DOMINATION IN JUMP GRAPHS

Abstract

A set D of vertices of a jump graph J(G) is a total efiient dominating set, if every vertex in V(J(G)) is adjacent to exactly one vertex in D. Total efficient domination number _teJ(G)) of J(G) is the minimum cardinality of a total efficient dominating set of J(G). In this paper the exact values of  _te (J(G)) for some standared graphs are found and some bounds are obtained .Also a Nordhus-Gadumm type result is obtained . In addition the total efficient domatic number d_te(J(G)) of J(G) is defined to be maximum order of a partition of the vertex set of J(G) into total efficient dominating set of J(G). Also a relation between (J(G) and  d_te(J(G)) is established.