For a simple connected graph G (V,E) , a non-empty subset S of V is a defensive alliance if each vS has at most one more neighbor in V S than it has in S and it is an offensive alliance if each vS has at least one more neighbor in S than it has outside of S . The least cardinality of any defensive alliance (offensive alliance) of G is called the defensive alliance number (offensive alliance number) of G , denoted as ad (G) (or ao(G) ). Further, a defensive alliance set (offensive alliance set) is called an accurate defensive alliance (accurate offensive alliance) in G if its complement has no defensive alliance set (offensive alliance set) of same cardinality. The least cardinality of an accurate defensive (or offensive) alliance in G is called an accurate defensive (or offensive) alliance number of G , denoted as aad (G) (or aao(G) ). In this paper we explore the bounds for accurate alliances in graphs and obtain accurate defensive (offensive) alliance number for some standard graphs. Also we characterize the graphs for accurate defensive (offensive) alliance number 1 and 2.
Volume 12 | Issue 4
Pages: 203-215
DOI: 10.5373/JARDCS/V12I4/20201434