The geodetic domination number of comb product graphs
| Main Authors: | Fahrudin, Dimas Agus; Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Indonesia, Saputro, Suhadi Wido; Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Indonesia |
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| Other Authors: | Program Hibah Desentralisasi, Penelitian Unggulan Perguruan Tinggi 586r/I1.C01/PL/2016 |
| Format: | Article info application/pdf eJournal |
| Bahasa: | eng |
| Terbitan: |
GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB
, 2020
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| Subjects: | |
| Online Access: |
https://www.ejgta.org/index.php/ejgta/article/view/1059 https://www.ejgta.org/index.php/ejgta/article/view/1059/pdf_146 |
Daftar Isi:
- 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.