A New Encryption Technique Using Detour Metric Dimension

V. Kala Devi, K. Marimuthu


A set of vertices \(W'\) detour resolves a graph \(G\) if every vertex is uniquely determined by its vector of detour distances to the vertices in \(W'\). A detour metric dimension of \(G\) is the minimum cardinality of a detour resolving set of \(G\). In this paper, detour metric dimension of certain graphs are investigated by detour distance matrix.


Detour resolving set; Detour metric dimension; Encryption and Decryption

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M. Baca, E.T. Baskoro, A.N.M. Salman, S.W. Saputro and D. Suprijanto, The metric dimension of regular bipartite graphs, Bull. Math. Soc. Sci. Math. Roumanie Tome 54(102) (1) (2011), 15 – 28.

J. Caceres, C. Hernando, M. Mora, M.L. Puertas, I.M. Pelayo, C. Seara and D.R. Wood, On the metric dimension of some families of graphs, Electronic Notes in Discrete Math. 22 (2005), 129 – 133.

G. Chartrand, C. Poisson and P. Zhang, Resolvability and the upper dimension of graphs, Comput. Math. Appl. 39 (2000), 19 – 28.

F. Harary and R.A. Melter, On the metric dimension of a graph, Ars Combin. 2 (1976), 191 – 195.

V. Kaladevi and P. Backiyalakshmi, Detour distance polynomial of Star Graph and Cartesian product of P2 £Cn, Antartica J. Math. 8(5) (2011), 399 – 406.

V. Kaladevi and P. Backialakshmi, Maximum distance matrix of super subdivision of star graph, Journal of Comp. & Math. Sci. 2(6) (2011), 828 – 835.

V. Kaladevi and S. Kavithaa, On varieties of reverse wiener like indices of a graph, Intern. J. Fuzzy Mathematical Archive 4(12) (2014), 37 – 46.

V. Kaladevi and S. Kavithaa, Fifteen reverse topological indices of a graph in a single distance matrix, Jamal Academic Research Journal, special issue (2014), pp. 1 – 9.

V. Kaladevi and K. Marimuthu, Relation between metric dimension and detour metric dimension for certain graphs, Jamal Academic Research Journal, special issue (2014), 441 – 447.

V. Kaladevi and P. Selvaani, Three polynomials in one matrix, Mathematical Sciences International Research Journal 1(1) (2012), 100 – 108.

P.J. Slater, Leaves of trees, Proc. 6th Southeastern Conf. on Combinatorics, Graph Theory and Computing, Vol. 14 of Congr. Number, 549 – 559, 1975.

P.J. Slater, Dominating and reference sets in a graph, J. Math. Phys. Sci. 22 (1998), 445 – 455.

DOI: http://dx.doi.org/10.26713%2Fjims.v9i3.1015

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