Performance On Topological Cordial Graphs

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Volume 1, Issue 1 (2021)

Published Online

January-February 2021

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11-12

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Research Article

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B.D. Acharya [3] introduced the documentation of set - valuation as set basic of number valuation as introduced by A. Rosa [5]. For a ( p, q ) outline G = ( V, E ) and a non-void set X of cardinality n. Acharya described set indexer of G as an injective set-regarded capacity f : V(G) → 2x so much that the ability f *: 𝐸 (𝐺) → 2𝑋 − {𝜙} portrayed by for every f * ( v1v2 ) = f( v1 ) ∆ f( v2 ) for each v1v2 ∈ 𝐸(𝐺) is moreover injective, where 2X is thesetofallsubsetsofXand∆isthesymmetricdifferenceofsets.ForagraphG,thereexistaset-indexerf:V(G)→ 2X so much that the familyf (V ) is a geology on X. An outline G = ( V, E ) should be a bitopological chart if there exist a set indexer f : V(G)→ 2x so much that f(V) and f * (E) ∪ {𝜙} are the two topographies on the relating groundset.LetGbeagraph.Define𝑓:(𝐺)→2𝑋suchthat{(𝑉(𝐺))}isatopologywhereXisanysetwith|𝑋| < 𝑛, number of vertices of G. The incited ability 𝑓∗on E(G) is portrayed by1 𝑖𝑓 (𝑢) ∩ (𝑣)𝑠 𝑛𝑜𝑡 𝑎𝑛 𝑒𝑚𝑝𝑡𝑦 𝑠𝑒𝑡 𝑎𝑛𝑑 𝑠𝑖𝑛𝑔𝑙𝑒𝑡𝑜𝑛 𝑠𝑒𝑡𝑓∗(𝑢𝑣) = 𝑓(𝑢) ∩ 𝑓(𝑣)={0 𝑖𝑓 𝑓(𝑢) ∩ 𝑓(𝑣) 𝑖𝑠 𝑎𝑛 𝑒𝑚𝑝𝑡𝑦 𝑎𝑛𝑑 𝑠𝑖𝑛𝑔𝑙𝑒𝑡𝑜𝑛𝑠𝑒𝑡.Further, |(0) − 𝑒𝑓(1)| ≤ 1 where 𝑒𝑓(0) = number of edges set apart with 0 and𝑒𝑓(1) = number of edges named with 1. We say that f is a topological merry naming and an outline which yields such a checking is called topological warm graph. In this paper we proved Gortzsch graph, vertex trading of cycle 𝐶𝑛, Bow diagram, David's Star outline are topolological cordialgraph. Key words: Gortzsch outline, vertex trading of cycle 𝐶𝑛, Bow graph, David's Star chart andtopolological ardent graph References 1. Acharya B.D., Set indexers of a graph and set – graceful graphs, Bull. Allahabad Math. Soc., 16 (2001),1-23 2. Acharya B.D, Germina K.A , Princy K.L and Rao S.B., Topologically set graceful graphs , Paper underrevision. 3. Acharya B.D., Set valuations and their applications, MRI Lecture note in Applied Mathematics, No.2, Mehta Research Institute of Mathematics and Mathematical Physics,1983. 4. GerminaK.A ,BindhuK.Thomas., On Bitopological Graphs, International Journel of Algorithm, Computing and Mathematics,vol.4 No.1, Feb.2011. 5. Haraey F., Graph Theory, Addison Wesley , reading Massachusetts,1969. 6. Rosa A., On certain valuations of the vertices of a graph ,Gorden and Breach, New York and Dunod, Paris, 1967, Proceedings of the International Symposium inRome.