Main Article Content
The metric dimension and dominating set are the concept of graph theory that can be developed in terms of the concept and its application in graph operations. One of some concepts in graph theory that combine these two concepts is resolving dominating number. In this paper, the definition of resolving dominating number is presented again as the term dominant metric dimension. The aims of this paper are to find the dominant metric dimension of some special graphs and corona product graphs of the connected graphs and , for some special graphs . The dominant metric dimension of is denoted by and the dominant metric dimension of corona product graph G and H is denoted by .
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Chartrand G, Eroh L, Johnson MA, Oellermann OR. Resolvability in graphs and the metric dimension of a graph. Discrete Appl. Math. 2000;105: 99-113.
Careres J, Hernando C, Mora M, Pelayo I, Puertas M, Seara C, et al. On the Metric Dimension of Cartesian Products of Graphs. SIAM . 2007; 21(2): 423-441.
Yero IG. Vertices, Edges, Distances and Metric Dimension of Graphs. ENDM . 2016; 55: 191-194.
Iswadi H. Batas Atas Bilangan Dominasi Lokasi Metrik Graf Hasil Operasi Korona. InProsiding Seminar Nasional Teknologi Informasi dan Multimedia 2011 (SNASTIA 2011) 2011 May 21 (pp. 1-5). University of Surabaya.
Saputro SW. On the Metric Dimension of Biregular Graph. JIP. 2017; 25: 634-638.
Susilowati L, Utoyo MI, Slamin S. On Commutative Characterization of Graph Operation with Respect to Metric Dimension. J. Math. Fund. Sci. 2017; 49(2): 156-170.
Gupta P, Goyal A, Jain R. Independent point-set dominating sets in graphs. AKCE Int. J. Graphs Comb. 2019; In Press.
Umilasari R, Darmaji D. Dominating number of Distance Two of Corona Product of Graphs. IJC. 2016; 1(1): 41-46.
Brigham RC, Chartrand G, Dutton RD, Zhang P. Resolving Domination in Graphs. Math. Bohem. 2003;128(1): 25–36.
González A, Hernando C, Mora M. Metric-locating-dominating sets of graph for constructing related subsets of vertex. Appl Math Comput. 2018; 332: 449-456.
Henning MA , Oellermann OR. Metric-Locating-Dominating Sets in Graphs. Ars Combinatoria. 2004; 73: 129-141
Iswadi H, Baskoro ET, Simanjuntak R. On the Metric Dimension of Corona Product Graphs. FJMS. 2011; 52(2): 155-170.
Susilowati L, Sa'adah I, Fauziyyah RZ, Erfanian A. The Dominant Metric Dimension of Graphs. Heliyon. 2020; 6: e03636.
Haynes TW, Hedetniemi S, Slater P. Fundamentals of Domination in Graphs. 1998; Marcel Dekker Inc, New York.