• TOTAL EFICIENT DOMINATION IN JUMP GRAPHS

N. PRATAP BABU RAO

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 dte(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  dte(J(G)) is established.


Keywords


Efficient dominating set, total dominating set, total efficient dominating set, total efficient domination number.

Full Text:

PDF


Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
© 2010-2019 International Journal of Mathematical Archive (IJMA)
Copyright Agreement & Authorship Responsibility
Web Counter