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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
Dimas Agus Fahrudin
Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Indonesia
Electrical & Electronics Engineering

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The geodetic domination number of comb product graphs Dimas Agus Fahrudin; Suhadi Wido Saputro
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 8, No 2 (2020): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2020.8.2.13

Abstract

A subset S of vertices in graph G is called a geodetic set if every vertex in V(G) \ S lies on a shortest path between two vertices in S. A subset S of vertices in G is called a dominating set if every vertex in V(G) \  S is adjacent to a vertex in S. The set S is called a geodetic dominating set if S is both geodetic and dominating sets. The geodetic domination number of G, denoted by γg(G), is the minimum cardinality of geodetic domination sets in G. The comb product of connected graphs G and H at vertex o ∈ V(H), denoted by  G ∇o H, is a graph obtained by taking one copy of G and |V(G)| copies of H and identifying the ith copy of H at the vertex o to the ith vertex of G. In this paper, we determine an exact value of γg(G ∇o H) for any connected graphs G and H.
Co-Authors Suhadi Wido Saputro