Assistant Professor, Department of Mathematics, Vivekananda College, Agasteeswaram, Kanyakumari District, Tamil Nadu, India.
A vertex v ∈ V (G) is said to be a self vertex switching of G if G is isomorphic to Gv, where Gv is the graph obtained from G by deleting all edges of G incident to v and adding all edges incident to v which are not in G. Duplication of a vertex v of graph G produces a new graph G′ by adding a new vertex v′ such that N(v′) = N(v). In other words a vertex v′ is said to be duplication of v if all the vertices which are adjacent to v in G are also adjacent to v′ in G′. A vertex v is called a duplication self vertex switching of a graph G if the resultant graph obtained after duplication of v has v as a self vertex switching. In this paper, we find duplication self vertex switchings of Pm x Pn.
switching, self vertex switching, duplication self vertex switching, dss1(G).
 Jayasekaran, C. Graphs with a given numn and eachber of self vertex switchings, International Journal of Algorithms, Computing and Mathematics, vol. 3(2010), no. 3, pp 27-36.
 Jayasekaran, C. Self vertex switchings of connected unicyclic graphs, Journal of Discrete Mathematical Sciences and Cryptography, vol. 15(2012), no. 6, pp. 377-388.
 Jayasekaran, C. Self vertex switchings of trees, Ars Combinatoria, 127(2016), pp. 33-43.
 Jayasekaran, C. Self vertex switchings of disconnected uni cyclic graphs, Ars Combinatoria, 129(2016), pp. 51-63.
 Jayasekaran, C. & Prabavathy, V. A characterisation of duplication self vertex switching in graphs, International Journal of Pure and Applied Mathematics, vol. 118, (2017), no. 2.
 Jayasekaran, C. & Prabavathy, V. Duplication self vertex switching in some graphs, (Communicated).
 Jayasekaran, C. & Prabavathy, V. Some results on duplication self vertex switchings, International Journal of Pure and Applied Mathematics, vol. 116(2017), no. 2, pp. 427-435.
 Lauri, J. Pseudosimilarity in graphs – a survey, Ars Combinatoria, 46(1997), pp. 77-95.
 Seidel, J., J. A survey of two graphs, in Proceedings of the Inter National Coll. Theorie combinatorie (Rome 1973), Tomo I, Acca. Naz. Lincei, (1976), pp. 481- 511.
 Stanley, R. Reconstruction from vertex switching, Combi. Theory. Series B, vol. 38 (1985), pp. 38-142.
 Vilfred, V., Paulraj Joseph, J. & Jeyasekaran, C. Branches and Joints in the study of self switching of graphs, The Journal of Combinatorial Mathematics and combinatorial Computing, 67 (2008), pp. 111-122.
 Vilfred, V. & Jayasekaran, C. Interchange similar self vertex switchings in graphs, Journal of Discrete Mathematical Sciences and Cryptography, vol. 12(2009), no. 4, pp. 467- 480.
To cite this article
Prabavathy, V. (2022). Duplication Self Vertex Switching of Pm x Pn. John Foundation Journal of EduSpark, 4(3), 34-38.