2011/12/05 by Saeid Alikhani, Alikhani, Saeid, Mohammad Hadi Akhbari +3 · 2 citations
Computer Science · Mathematics · #05C69 #11B83 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Graph theory and applications
paper · pdf · doi:10.48550/arxiv.1112.0846
openalex publication_date 2011/12/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G=(V,E) be a simple graph. A set S⊆ V(G) is called an outer-connected dominating set (or ocd-set) of G, if S is a dominating set of G and either S=V(G) or V\backslash S is a connected graph. In this paper we introduce a polynomial which its coefficients are the number of ocd-sets of G. We obtain some properties of this polynomial and its coefficients. Also we compute this polynomial for some specific graphs.