PAIR DIFFERENCE CORDIALITY OF MIRROR GRAPH,SHADOW GRAPH AND SPLITTING GRAPH OF CERTAIN GRAPHS

Abstract

In this paper we dicuss the pair difference cordility of Mirror graph, Splitting graph, Shadow graph of some graphs. we have studied about the pair difference cordility of Mirror graph, Splitting graph, Shadow graph of some graphs.Investigation of the pair difference cordility of Mirror graph, Splitting graph, Shadow graph of some special graphs are the open problems.

Keywords

• path
• cycle
• mirror graph

References

1. I.Cahit., Cordial Graphs : A weaker version of Graceful and Harmonious graphs, Ars combin., 23 (1987), 201-207.
2. I.Cahit., On cordial and 3-equitable labellings of graphs, Util.Math., 37 (1990), 189-198.
3. I.Cahit., Some Totally modular cordial graphs, Discussion.Math.Graph Theory, 22 (2002), 247-258.
4. Ebrahim Salehi.,Seth Churchman.,Tahj Hill.,Jim Jordan., Product Cordial Sets of Trees, Congressus Numerantium, 220 (2014), 183-193.
5. Ebrahim Salehi., Product Cordial Sets of Long Grids, Ars combin., 107 (2012), 339-351.
6. J.A. Gallian., A Dynamic survey of graph labeling, The Electronic Journal of Combinatorics., 19, (2016).
7. R.L.Graham., and N.J,A.Solane., On additive bases and harmonious graphs, SIAM J.Alg.Disrete Methods., 1, (1980) 382-404.
8. F.Harary., Graph theory, Addision wesley, New Delhi, 1969.

9. R.Ponraj., A.Gayathri., and S.Soma Sundaram., Pair difference cordial labeling of graphs, J.Math. Comp.Sci. Vol.11(1), (2015), 189-197.
10. U.M.Prajapati, U.M., and S.J.Gajjar., Cordial labeling for complement graphs,Mathematics Today Vol.30, (2015), 99-118.
11. U.M.Prajapati., and S. J. Gajjar., Some results on prime cordial labeling of generalized prism graph Ym;n,Ultra Scientist Vol.27(3)A , (2015), 189-204.
12. U.M.Prajapati., Prakruti D.Shah., Some Edge Product Cordial graphs in the context of Duplication of some Graph Elements, Open Journal of Discrete Mathematics , (6), (2016), 248-258.
13. U.M.Prajapati., N.B.Patel., Edge Product Cordial labeling of Some Cycle Related Graphs, Open Journal of Discrete Mathematics , (6), (2016), 268-278.
14. U.M.Prajapati., N.B.Patel., Edge Product Cordial labeling of Some Graphs, Journal of Applied Mathematics and Computer Mechanics Discrete Mathematics ,(Vol18)(1), (2019), 69-76.
15. A. Rosa., On certain Valuations of the vertices of a graph,Theory of Graphs, International Symposium,Rome., July, (1967) 349-345.
16. J.Sedlacek., Problem 27, in Theory Graphs and its Applications, Proc.Symposium Smolenice., June, (1963) 163-167.
17. M.A.Seoud., E.F.Helmi., On Product cordial graphs, Ars.Combin, Vol.101, (2011), 519-529.
18. M.A.Seoud., M.S.Salman., Some results and examples on difference cordial graphs, Turkish Journal of Mathematics, 40, (2016), 417-427.
19. S.Somasundaram., and R.Ponraj., Mean Labeling of Graphs, Natl.Acad.sci.Let., 26, (2003),210-213.