The Upper Total Restrained Edge Geodetic Domination Number Of A Graph

  • P. Arul Paul Sudhahar and R. Umamaheswari

Abstract

A setof vertices of a connected graphis a restrained geodetic dominatingset,if either oris a geodetic dominating set with the subgraphinduced byhas no isolated vertices. The minimum cardinality of a restrained geodetic dominating set of  is called the restrained geodetic domination number and is denoted byA total restrained edge geodetic dominating set S in a connected graph G is called a minimal total restrained edgegeodetic dominating set of G, if no proper subset of S is a total restrained edge geodetic dominating set of G . The upper total restrained edgegeodetic domination numberis the maximum cardinality of a minimal total restrained edge geodetic dominating set of G.The upper total restrained geodetic domination number of certain classes of graphs are determined.It is shown that for every pair of integersa, b  with, there exists a connected graph G of order bsuch that.  Also, for any five  integers a, b, c ,d  and ewith   there exists a connected graph Gsuch that ,  ,  ,and

Published
2020-05-19
How to Cite
P. Arul Paul Sudhahar and R. Umamaheswari. (2020). The Upper Total Restrained Edge Geodetic Domination Number Of A Graph. International Journal of Advanced Science and Technology, 29(7s), 2660 - 2668. Retrieved from https://sersc.org/journals/index.php/IJAST/article/view/16752