2018/12/07 by Mostafa Tavakoli, Tavakoli, Mostafa, Sandi Klavžar +1
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Graph theory and applications #math.CO
paper · pdf · doi:10.48550/arxiv.1812.02992
arxiv created 2018/12/07 · openalex publication_date 2018/12/07 · arxiv updated 2018/12/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
If G=(VG, EG) is a graph, then S⊆ VG is a global defensive k-alliance in G if (i) each vertex not in S has a neighbor in S and (ii) each vertex of S has at least k more neighbors inside S than outside of it. The global defensive k-alliance number of G is the minimum cardinality among all global defensive k-alliance in G. In this paper this concept is studied on the generalized hierarchical, the lexicographic, the corona, and the edge corona product. For all of these products upper bounds expressed with related invariants of the factors are given. Sharpness of the bounds are also discussed.