| Abstrakt: |
For a graph G = (V, E), a defensive alliance of G is a set of vertices S ⊆ V(G) satisfying the condition that for each v ∈ S, at least half of the vertices in the closed neighborhood of v are in S. Let φ: V(G) → {1, 2, 3, ..., |V|} be a bijection. A subset S ⊆ V is called difference secure set of G with respect to φ if for all u, v ∈ S, there is a w ∈ S such that |φ(u) - φ(v)| = φ(w) if and only if uv ∈ E. A defensive alliance S of G which is also a difference secure set is called defensive alliance difference secure set. In this paper, we compute the maximum cardinality of various types of minimal defensive alliance difference secure sets for paths. [ABSTRACT FROM AUTHOR] |
