On Graph Domination Numbers

Abstract

In this paper, we determine for a simple graph G on n vertices and m edges a variety of domination parameters such as connected domination number, outer connected domination number, doubly connected domination number, global domination number, total global connected domination number, 2-connected domination number, strong domination number, fair domination number, independence domination number etc.

Computation of Various Domination Numbers of Rolf Nevanlinna (RNP) Collaboration Graph

“…The maximum cardinality of a 2-packing set of G is called the 2-packing number of G and is denoted by  2 (G). 6 ), e 6 = (u 1 , u 7 ), e 7 = (u 1 , u 8 ), e 8 = (u 1 , u 9 ), e 9 = (u 1 , u 10 ), e 10 = (u 2 , u 8 ), e 11 = (u 2 , u 13 ), e 12 = (u 2 , u 14 ), e 13 = (u 2 , u 17 ), e 14 = (u 2 , u 18 ), e 15 = (u 3 , u 11 ), e 16 = (u 4 , u 12 ), e 17 = (u 5 , u 16 ), e 18 = (u 6 , u 9 ), e 19 = (u 6 , u 16 ), e 20 = (u 6 , u 17 ), e 21 = (u 7 , u 8 ), e 22 = (u 7 , u 9 ), e 23 = (u 7 , u 17 ), e 24 = (u 7 , u 18 ), e 25 = (u 8 , u 9 ), e 26 = (u 8 , u 13 ), e 27 = (u 8 , u 17 ), e 28 = (u 8 , u 18 ), e 29 = (u 9 , u 10 ), e 30 = (u 9 , u 17 ), e 31 = (u 9 , u 19 ), e 32 = (u 10 , u 13 ), e 33 = (u 11 , u 15 ), e 34 = (u 12 , u 15 ), e 35 = (u 13 , u 17 ), e 36 = (u 13 , u 18 ), e 37 = (u 13 , u 19 ), e 38 = (u 13 , u 20 ), e 39 = (u 16 , u 17 ), e 40 = (u 17 , u 19 ), e 41 = (u 19 , u 20 ), e 42 = (u 1 , u 21 ), e 43 = (u 7 , u 21 ), e 44 = (u 9 , u 21 ), e 45 = (u 17 , u 22 ), e 46 = (u 19 , u 21 ), e 47 = (u 21 , u 22 ), e 48 = (u 22 , u 23 ). None of the eight RNPW'S have Erdos number 1.…”