Authors :
Denizar Kemala; Nurdin; Muhammad Zakir
Volume/Issue :
Volume 9 - 2024, Issue 6 - June
Google Scholar :
https://tinyurl.com/yc8nsjya
Scribd :
https://tinyurl.com/3mvwxtm5
DOI :
https://doi.org/10.38124/ijisrt/IJISRT24JUN485
Note : A published paper may take 4-5 working days from the publication date to appear in PlumX Metrics, Semantic Scholar, and ResearchGate.
Abstract :
For example, G is a connected graph and W is
a subset of the set of points V on G. Set W is called the
determining set on G if every point on G has different
representations towards W. A determining set with a
minimum number of members is called a minimum
determining set or the basis of G and the cardinality of
the minimum determinant set represents the metric
dimension of the graph G. And denoted by dim(G).
This paper discusses the metric dimensions of
modified hourglass graphs mHgn constructed from a
complete graph K1 with graphs Cn. Based on the results
of the discussion, it was found that dim (mHgn) with m ≥
3 and 3 ≤ n ≤ 5 is 2m.
Keywords :
Hourgand Graph, Metric Dimensions, Trajectory Graph.
References :
- F. Harary, Graf Theory, USA: Addision Wesley Publishing Company, 1994.
- F. M. R. A. Harary, ""On the metric dimension of a graph,,"," Ars Combinatoria, pp. p. 2: 191 -195,, 1976.
- G. Chartrand and L. Lesniak, graphs and digraphs third edition, United State of America: Chapman & Hall, 2000.
- Hasmawati, Pengantar dan jenis-jenis Graf, Makassar: Unhas Press, 2020.
- R. Wijaya, "Dimensi Metrik Hasil Identifikasi," Jurnal matematika UNAD, vol. 11, pp. 199-209, 2022.
- Syamsuddin, "Bilangan Ramsey Multipartit Ukuran untuk Graf Lintasan versus Graf Jam Pasir," 2023.
- S. M. Saputro, "Th metric Dimension of Comb Products Graphs," in Graphs theory Conference in Honor of Egawa's 60th Birthday, september 10 to 14.
- G. Chartrand, Introductory Graph Theory, Dover, 1985.
- Clark and D. A. Hoiton, A First Look at Graph Theory, World Scientific Publishing, 1991.
- F. Harary, R. Z. Norman and D. Cartwright, Structural Models, Wiley, 1965.
- O. Ore, Graphs and their Uses, 2nd edn, New Mathematical Library 10, Mathematical Association of America, 1990.
- R. J. Wilson and J. J. Watkins, Graphs; An Introductory Approach, Wiley, 1990.
For example, G is a connected graph and W is
a subset of the set of points V on G. Set W is called the
determining set on G if every point on G has different
representations towards W. A determining set with a
minimum number of members is called a minimum
determining set or the basis of G and the cardinality of
the minimum determinant set represents the metric
dimension of the graph G. And denoted by dim(G).
This paper discusses the metric dimensions of
modified hourglass graphs mHgn constructed from a
complete graph K1 with graphs Cn. Based on the results
of the discussion, it was found that dim (mHgn) with m ≥
3 and 3 ≤ n ≤ 5 is 2m.
Keywords :
Hourgand Graph, Metric Dimensions, Trajectory Graph.
