Bondage number of mesh networks

Abstract

Abstract:The bondage number b(G) of a nonempty graph G is the smallest number of edges whose removal from G results in a graph with domination number greater than that of G. Denote P n ×P m be the Cartesian product of two paths P n and P m . This paper determines that the exact value of b(P n × P 2 ), b(P n × P 3 ) and b(P n × P 4 ) for n ≥ 2.

On Bondage Numbers of Graphs: A Survey with Some Comments

“…The bondage number of × for ⩾ 4 and 2 ⩽ ⩽ 4 is determined as follows (Li [39] also determined ( × 2 )). [40], 2012). For ⩾ 4,…”

Bondage Number of Lexicographic Product of Two Graphs

“…In [9], Hartnell and Rall have proved b(Gn) =3/4 ∆, for the cartesian product Gn = Kn □ Kn, n > 1. In [14], Hu and Xu have determined the bondage numbers of Cartesian product of two paths Pn and Pm for n ≥ 2, m ≤ 4. In [16], Kang et al have proved b(C n □ C 4 ) = 4, n ≥ 4 for discrete torus C n □ C 4 .…”

The bondage number of the strong product of a complete graph with a path and a special starlike tree

“…For example, b(K n K n ) for n ≥ 3 [6,16], b(C n P 2 ) for n ≥ 3 [3], b(C n C 3 ) for n ≥ 4 [15], b(C n C 4 ) for n ≥ 4 [12], b(C n C 5 ) for n ≡ 3 (mod 5) and n ≥ 5 [2], b(P n P 2 ), b(P n P 3 ) and b(P n P 4 ) for n ≥ 2 [9] have been determined.…”