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All Journal Electronic Journal of Graph Theory and Applications (EJGTA) Indonesian Journal of Combinatorics
Suhadi Wido Saputro
Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Indonesia
Computer Science & IT Decision Sciences, Operations Research & Management 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.
The total vertex irregularity strength of symmetric cubic graphs of the Foster's Census Rika Yanti; Gregory Benedict Tanidi; Suhadi Wido Saputro; Edy Tri Baskoro
Indonesian Journal of Combinatorics Vol 6, No 2 (2022)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/ijc.2022.6.2.3

Abstract

Foster (1932) performed a mathematical census for all connected symmetric cubic (trivalent) graphs of order n with n ≤ 512. This census then was continued by Conder et al. (2006) and they obtained the complete list of all connected symmetric cubic graphs with order n ≤ 768. In this paper, we determine the total vertex irregularity strength of such graphs obtained by Foster. As a result, all the values of the total vertex irregularity strengths of the symmetric cubic graphs of order n from Foster census strengthen the conjecture stated by Nurdin, Baskoro, Gaos & Salman (2010), namely ⌈(n+3)/4⌉.
Co-Authors Dimas Agus Fahrudin Edy Tri Baskoro Gregory Benedict Tanidi Rika Yanti