Concepts Arising from Strong Efficient Domination Number. Part II

ABSTRACT

Let G = (V,E) be a simple graph. A subset S of V(G) is called a strong (weak) efficient dominating set of G if for every v∈𝑉(𝐺),|𝑁𝒔[𝒗]∩𝑆|=1.( |𝑁𝑤[𝑣]∩𝑆|=1), where 𝑁𝑠(𝑣)={𝑢∈𝑉(𝐺):𝑢𝑣∈𝐸(𝐺),𝑑𝑒𝑔𝑢≥𝑑𝑒𝑔𝑣}(𝑁𝑤(𝑣){𝑢∈𝑉(𝐺),𝑢𝑣∈𝐸(𝐺),𝑑𝑒𝑔𝑣≥𝑑𝑒𝑔𝑢}. The minimum cardinality of a strong (weak) efficient dominating set of G is called the strong (weak) efficient domination number of G and denoted by 𝛾𝑠𝑒(𝐺)(𝛾𝑤𝑒(𝐺)). The strong efficient non bondage number 𝑏𝑠𝑒𝑛(𝐺) is the maximum cardinality of all sets of edge 𝑋⊆𝐸 such that 𝛾𝑠𝑒(𝐺−𝑋) = 𝛾𝑠𝑒(𝐺). In this paper, the strong efficient non bondage number of some corona related graphs are studied.