• TOTAL EFFICIENT DOMINATION IN GRAPHS

V. R. KULLI*, D. K. PATWARI

Abstract


A set D of vertices of a graph G is a total efficient dominating set if every vertex in V is adjacent to exactly one vertex in D. The total efficient domination number gte(G) of G is the minimum cardinality of a total efficient dominating set of G. In this paper, the exact values of gte(G) for some standard graphs are found and some bounds are obtained. Also a Nordhaus-Gaddum type result is established. In addition, the total efficient domatic number dte(G) of G is defined to be maximum order of a partition of the vertex set of G into total efficient dominating sets of G. Also a relation between gte(G) and dte(G) is established.


Keywords


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

Full Text:

PDF

Refbacks

  • There are currently no refbacks.


Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
© 2011-2019 Research Journal of Pure Algebra (RJPA)
Copyright Agreement & Authorship Responsibility
HTML Counter
Counter