2024/07/09 by Dilbak Haje, Delbrin Ahmed, Haje, Dilbak +5
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Graph theory and applications
paper · pdf · doi:10.48550/arxiv.2407.07182
openalex publication_date 2024/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G=(V,E) be a finite connected simple graph with vertex set V and edge set E. A signed Roman dominating function (SRDF) on a graph G is a function f: V → \-1, 1, 2\ that satisfies two conditions: (i) ∑y∈ N[x] f(y)≥1 for each x∈ V, where the set N[x] is the closed neighborhood of x consisting of x and vertices of V that are adjacent to x, and (ii) each vertex x∈ V where f(x) = -1 is adjacent to at least one vertex y∈ V where f(y)=2. The weight of a SRDF is the sum of its function values over all vertices. The signed Roman domination number of G, denoted by γSR(G), is the minimum weight of a SRDF on G. In this paper, we investigate the signed Roman domination number of the Ladder graph LGn, the circular Ladder graph CLn and their complements.