Computing the Metric Dimension of Gear Graphs
AbstractLet G = (V, E) be a connected graph and d(u, v) denote the distance between the vertices u and v in G. A set of vertices W resolves a graph G if every vertex is uniquely determined by its vector of distances to the vertices in W. A metric dimension of G is the minimum cardinality of a resolving set of G and is denoted by dim(G). Let J2n,m be a m-level gear graph obtained by m-level wheel graph W2n,m ≅ mC2n + k1 by alternatively deleting n spokes of each copy of C2n and J3n be a generalized gear graph obtained by alternately deleting 2n spokes of the wheel graph W3n. In this paper, the metric dimension of certain gear graphs J2n,m and J3n generated by wheel has been computed. Also this study extends the previous result given by Tomescu et al. in 2007. View Full-Text
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Imran, S.; Siddiqui, M.K.; Imran, M.; Hussain, M.; Bilal, H.M.; Cheema, I.Z.; Tabraiz, A.; Saleem, Z. Computing the Metric Dimension of Gear Graphs. Symmetry 2018, 10, 209.
Imran S, Siddiqui MK, Imran M, Hussain M, Bilal HM, Cheema IZ, Tabraiz A, Saleem Z. Computing the Metric Dimension of Gear Graphs. Symmetry. 2018; 10(6):209.Chicago/Turabian Style
Imran, Shahid; Siddiqui, Muhammad K.; Imran, Muhammad; Hussain, Muhammad; Bilal, Hafiz M.; Cheema, Imran Z.; Tabraiz, Ali; Saleem, Zeeshan. 2018. "Computing the Metric Dimension of Gear Graphs." Symmetry 10, no. 6: 209.
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