Metric dimension of generalized wheels
In a graph G, a vertex w∈V(G) resolves a pair of vertices u,v∈V(G) if d(u,w)≠d(v,w). A resolving set of G is a set of vertices S such that every pair of distinct vertices in V(G) is resolved by some vertex in S. The minimum cardinality among all the resolving sets of G is called the metric dimension...
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| Published in | Arab journal of mathematical sciences Vol. 25; no. 2; pp. 131 - 144 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier B.V
01.07.2019
Emerald Publishing |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1319-5166 2588-9214 |
| DOI | 10.1016/j.ajmsc.2019.04.002 |
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| Abstract | In a graph G, a vertex w∈V(G) resolves a pair of vertices u,v∈V(G) if d(u,w)≠d(v,w). A resolving set of G is a set of vertices S such that every pair of distinct vertices in V(G) is resolved by some vertex in S. The minimum cardinality among all the resolving sets of G is called the metric dimension of G, denoted by β(G). The metric dimension of a wheel has been obtained in an earlier paper (Shanmukha et al., 2002). In this paper, the metric dimension of the family of generalized wheels is obtained. Further, few properties of the metric dimension of the corona product of graphs have been discussed and some relations between the metric dimension of a graph and its generalized corona product are established. |
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| AbstractList | In a graph G, a vertex w∈V(G)resolves a pair of vertices u,v∈V(G)if d(u,w)≠d(v,w). A resolving set of G is a set of vertices S such that every pair of distinct vertices in V(G)is resolved by some vertex in S. The minimum cardinality among all the resolving sets of G is called the metric dimension of G, denoted by β(G). The metric dimension of a wheel has been obtained in an earlier paper (Shanmukha et al., 2002). In this paper, the metric dimension of the family of generalized wheels is obtained. Further, few properties of the metric dimension of the corona product of graphs have been discussed and some relations between the metric dimension of a graph and its generalized corona product are established. Keywords: Resolving set, Metric dimension, Generalized wheel, Corona product, Mathematics Subject Classification: 05C56, 05C12 In a graph G, a vertex w∈V(G) resolves a pair of vertices u,v∈V(G) if d(u,w)≠d(v,w). A resolving set of G is a set of vertices S such that every pair of distinct vertices in V(G) is resolved by some vertex in S. The minimum cardinality among all the resolving sets of G is called the metric dimension of G, denoted by β(G). The metric dimension of a wheel has been obtained in an earlier paper (Shanmukha et al., 2002). In this paper, the metric dimension of the family of generalized wheels is obtained. Further, few properties of the metric dimension of the corona product of graphs have been discussed and some relations between the metric dimension of a graph and its generalized corona product are established. |
| Author | Kunikullaya, Shreedhar Sooryanarayana, Badekara Swamy, Narahari Narasimha |
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| Cites_doi | 10.1023/A:1025745406160 10.1016/j.dam.2011.12.009 10.1016/S0166-218X(00)00198-0 10.1016/0166-218X(95)00106-2 |
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| Keywords | Resolving set 05C56 05C12 Generalized wheel Corona product Metric dimension |
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| References | Sooryanarayana, Shreedhar, Narahari (b13) 2016; 4 Khuller, Raghavachari, Rosenfeld (b6) 1996; 70 Grigorious, Kalinowski, Ryan, Stephen (b4) 2017; 69 Shanmukha, Sooryanarayana, Harinath (b7) 2002; 8 Sooryanarayana, Shreedhar, Narahari (b14) 2016; 22 Harary, Melter (b5) 1976; 2 Sooryanarayana (b11) 2012 Shreedhar, Sooryanarayana, Hegde, Vishukumar (b8) 2010; 4 Sooryanarayana, Geetha (b12) 2014; 4 Cáceres, Hernando, Mora, Pelayo, Puertas (b2) 2009; 160 Slater (b9) 1975; 14 Buczkowski, Chartrand, Poisson, Zhang (b1) 2003; 46 Chartrand, Eroh, Johnson, Oellermann (b3) 2000; 105 Sooryanarayana (b10) 1998; 29 Shreedhar (10.1016/j.ajmsc.2019.04.002_b8) 2010; 4 Sooryanarayana (10.1016/j.ajmsc.2019.04.002_b13) 2016; 4 Cáceres (10.1016/j.ajmsc.2019.04.002_b2) 2009; 160 Khuller (10.1016/j.ajmsc.2019.04.002_b6) 1996; 70 Buczkowski (10.1016/j.ajmsc.2019.04.002_b1) 2003; 46 Grigorious (10.1016/j.ajmsc.2019.04.002_b4) 2017; 69 Slater (10.1016/j.ajmsc.2019.04.002_b9) 1975; 14 Sooryanarayana (10.1016/j.ajmsc.2019.04.002_b14) 2016; 22 Sooryanarayana (10.1016/j.ajmsc.2019.04.002_b11) 2012 Sooryanarayana (10.1016/j.ajmsc.2019.04.002_b12) 2014; 4 Harary (10.1016/j.ajmsc.2019.04.002_b5) 1976; 2 Sooryanarayana (10.1016/j.ajmsc.2019.04.002_b10) 1998; 29 Shanmukha (10.1016/j.ajmsc.2019.04.002_b7) 2002; 8 Chartrand (10.1016/j.ajmsc.2019.04.002_b3) 2000; 105 |
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| Snippet | In a graph G, a vertex w∈V(G) resolves a pair of vertices u,v∈V(G) if d(u,w)≠d(v,w). A resolving set of G is a set of vertices S such that every pair of... In a graph G, a vertex w∈V(G)resolves a pair of vertices u,v∈V(G)if d(u,w)≠d(v,w). A resolving set of G is a set of vertices S such that every pair of distinct... |
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| SubjectTerms | Corona product Generalized wheel Metric dimension Resolving set |
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| Title | Metric dimension of generalized wheels |
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