Computing the strong alliance polynomial of a graph

الأصل · EN

We introduce the strong alliance polynomial of a graph. The strong alliance polynomial of a graph G with order n and strong defensive alliance number a(G) is the polynomial a(G;x):=∑ᵢ₌ₐ₍G₎ⁿ aᵢ(G)xⁱ, where aₖ(G) is the number of strong defensive alliances with cardinality k in G. We obtain some properties of a(G; x) and its coefficients. In particular, we compute strong alliance polynomial for path, cycle, complete, start, complete bipartite and double star graphs; some of them verify unimodality.