Path Relatively Prime Cordial Graph
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1 World Journal of Research and Review (WJRR) ISSN: , Volume-3, Issue-2, August 2016 Pages Path Relatively Prime Cordial Graph Dr. A. Nellai Murugan,V.Nishanthini Abstract be a graph with vertices and edges. A Analytic Mean Cordial Labeling of a Graph G with vertex set is a bijection from edge labelling are defined by.the induced if either divides (or) divides one otherwise and if any one of the vertex label is, the induced edge label is. The graph that admits a Relatively Prime Cordial Graph is called Relatively Prime Cordial Graph. In this paper, we proved that path related graphs,, + are Relatively Prime Cordial Graph. Index Terms Relatively Prime Cordial Graph, Relatively Prime Cordial Labeling. I. INTRODUCTION A graph is a finite non-empty set of objects called vertices together with a set of unordered pairs of distinct vertices of which is called edges. Each pair of vertices in is called an edge or a line of in which is said to join and. We write and say that and are adjacent vertices (sometimes denoted as ); vertex and the edge are incident with each other, as are and. If two distinct edges and are incident with a common vertex, then they are called. A graph with vertices and edges is called graph. In this paper,we proved that path related graphs,, + are Relatively Prime Cordial Graph. For graph theory terminology, we follow [2]. II.PRELIMINARIES be a graph with vertices and edges. A Analytic Mean Cordial Labeling of a Graph G with vertex set is a bijection from.the induced edge labelling are defined by if either divides (or) divides one otherwise and if any one of the vertex label is, the induced edge label is. The graph that admits a Relatively Prime Cordial Graph is called Relatively Prime Cordial Graph. In this paper, we proved that path related graphs,, + are Relatively Prime Cordial Graph. Definition: 2.1 is a path of length. Definition: 2.2 The Corona of two graph and is defined as the graph obtained by taking one copy of (which has points) and copies of and joining the point of to every point in the copy of,the graph is called a. Definition: 2.3 is a path of length n-1 of twice. Definition: 2.4 Star of length one is joined with every vertex of a path through an edge. It is denoted by Definition: 2.5 The join of and is the graph G = + with vertex set V = U and edge set E = U U{UV :u,v }.The graph + is called a Fan. II. MAIN RESULTS THEOREM: 3.1 Path is Relatively Prime Cordial Graph. be The vertex labeling are The induced edge labeling are, Dr. A.Nellai Murugan, Dept. of Mathematics, V.O. Chidambaram College, Tuticorin. V.Nishanthini, Dept. of Mathematics, V.O. Chidambaram College, Tuticorin. 74
2 Path Relatively Prime Cordial Graph Here, be Graph, m>1 Hence, Path is Relatively Prime Cordial Graph. THEOREM: 3.2 be is a Relatively Prime Cordial Graph. Edge Labeling: The vertex labeling are, The induced edge labeling are, Here, For example, Relatively Prime Cordial Graph, are shown in the fig Hence, Path is a Relatively Prime Cordial Graph. THEOREM: 3.3 Graph is a Relatively Prime Cordial Graph. 75
3 World Journal of Research and Review (WJRR) ISSN: , Volume-3, Issue-2, August 2016 Pages THEOREM: 3.4 Graph is a Relatively Prime Cordial Graph. Edge Labeling:1 Here,, m>1 Edge labeling: Here, THEOREM: 3.5 Graph is Relatively Prime Cordial graph. REFERENCES [1] Gallian J.A, A Dynamic Survey of Graph Labelling, The Electronic Journal of Combinatorics, 6 (2001) #DS6 [2] Harray. F, Graph Theory, Adadison-Wesley Publishing Company Inc, USA, 1969 [3] A.Nellai Murugan and V.Baby Suganya, A study on cordial labeling of Splitting Graphs of star Attached C3 and (2k+1)C3 ISSN , Outreach, A Multi Disciplinary Refreed Journal, Volume. VII, 2014, I.F [4] A.Nellai Murugan and V.Brinda Devi, A study on Star Related Divisor cordial Graphs,ISSN , Outreach, A Multi Disciplinary Refreed Journal, Volume. VII, 2014, I.F [5] A.Nellai Murugan and M. Taj Nisha, A study on Divisor Cordial Labeling Star Attached Path Related Graphs, ISSN , Outreach, A Multi Disciplinary Refreed Journal, Volume. VII, 2014, I.F [6] A. Nellai Murugan and V.Sripratha, Mean Square Cordial Labelling, International Journal of Innovative Research & Studies, ISSN ,Volume 3, Issue 10Number 2,October 2014, PP [7] A.Nellai Murugan and A.L Poornima,Meanness of Special Class Of Graphs, International Journal of Mathematical Archive. ISSN , Vol 5, issue 8, 2014, PP [8] A.Nellai Murugan and A.Mathubala, Path Related Homo- cordial graphs, International Journal of Innovative Science, Engineering & Technology, ISSN ,Vol.2, Issue 8,August. 2015,PP IF 1.50,IBI-Factor 2.33 [9] A.Nellai Murugan,V.Selva Vidhya and M Mariasingam, Results On Hetro- cordial graphs, International Journal of Innovative Science, Engineering & Technology, ISSN ,Vol.2, Issue 8,August. 2015,PP IF 1.50,IBI-Factor
![A, A Dynamic Survey of Graph Labelling, The Electronic Journal of Combinatorics, 6 (2001) #DS6 [2] Harray. F, Graph Theory, Adadison-Wesley Publishing Company Inc, USA, 1969 [3] A.](/docs-images/46/23537048/images/page_3.jpg "Nellai Murugan and V.Baby Suganya, A study on cordial labeling of Splitting Graphs of star Attached C3 and (2k+1)C3 ISSN 2321 8835, Outreach, A Multi Disciplinary Refreed Journal, Volume.")
4 Path Relatively Prime Cordial Graph [10] A.Nellai Murugan, and R.Megala, Path Related Relaxed Cordial Graphs, International Journal of Scientific Engineering and Applied Science (IJSEAS) - ISSN: ,Volume-1, Issue-6, September,2015,PP IF ISRA [11] A.Nellai Murugan and J.Shiny Priyanka, Tree Related Extended Mean Cordial Graphs, International Journal of Research -Granthaalayah, ISSN ,Vol.3, Issue 9,September. 2015, PP I.F (I2OR). [12] A.Nellai Murugan and S.Heerajohn, Cycle Related Mean Square Cordial Graphs, International Journal Of Research & Development Organization Journal of Mathematics,Vol.2, Issue 9,September. 2015, PP [13] A.Nellai Murugan and A.Mathubala, Special Class Of Homo- Cordial Graphs, International Journal Emerging Technologies in Engineering Research, ISSN ,Vol.2, Issue 3,October 2015, PP 1-5. [14] A.Nellai Murugan, and R.Megala,Tree Related Relaxed Cordial Graphs, International Journal of Multi disciplinary Research & Development, ISSN: ,Volume-2, Issue-10, October,2015,PP IF [15] A.Nellai Murugan, and A.Mathubala,Cycle Related Homo-Cordial Graphs, International Journal of Multi disciplinary Research & Development, ISSN: ,Volume-2, Issue-10, October,2015,PP IF [16] L. Pandiselvi, A. Nellai Murugan, and S. Navaneethakrishnan, Some Results on Near Mean Cordial, Global Journal of Mathematics, ISSN ,Volume 4,No : 2,August-2015, PP [17] A.Nellai Murugan and V.Selvavidhya, Path Related Hetro- Cordial Graphs, International Journal Emerging Technologies in Engineering Research, ISSN ,Vol.2, Issue 3,October 2015, PP [18] A.Nellai Murugan and S.Heerajohn, Special Class of Mean Square Cordial Graphs, International Journal Of Applied Research,ISSN ,Vol.1, Issue 11,Part B, October 2015, PP I F 5.2 [19] A.Nellai Murugan and J.Shinny Priyanka, Extended Mean Cordial Graphs of Snakes,International Journal Emerging Technologies in Engineering Research, ISSN ,Vol.3, Issue 1,October 2015, PP [20] A.Nellai Murugan and R.Megala Special Class of Relaxed Cordial Graphs,International Journal Emerging Technologies in Engineering Research, ISSN ,Vol.3, Issue 1,October 2015, PP [21] A.Nellai Murugan and P. Iyadurai Selvaraj, Cycle and Armed Cap Cordial graphs, Global Scholastic Research Journal of Multidisciplinary, ISSN ,Volume, Issue 11, October 2015, PP ISRA [22] A.Nellai Murugan and J.Shinny Priyanka, Path Related Extended Mean Cordial Graphs,International Journal of Resent Advances in Multi- Disciplinary Research, ISSN ,Vol.2, Issue 10,October 2015, PP I F [23] A.Nellai Murugan and G.Devakiruba., Divisor cordial labeling of Book and K1,n., OUTREACH, A Multi-Disciplinary Refereed Journal, Volume VIII, 2015, Pp [24] A. Nellai Murugan and P. Iyadurai Selvaraj, Path Related Cap Cordial Graphs, OUTREACH, A Multi- Disciplinary Refereed Journal, Volume VIII, 2015, Pp [25] A. Nellai Murugan, and A.Meenakshi Sundari, Product Cordial Graph of Umbrella and Sn., OUTREACH, A Multi-Disciplinary Refereed Journal, Volume VIII, 2015, Pp [26] A. Nellai Murugan, and V.Sripratha, Mean Square Cordial Labeling, OUTREACH, A Multi-Disciplinary Refereed Journal, Volume VIII, 2015, Pp [27] A.Nellai Murugan and A.L.Poornima, Meanness of Special Class of Graph, OUTREACH, A Multi-Disciplinary Refereed Journal, Volume VIII, 2015, Pp [28] A.Nellai Murugan and G.Esther, Mean Cordial Labeling of Star, Bi-Star and Wheel, OUTREACH, A Multi-Disciplinary Refereed Journal, Volume VIII, 2015, Pp [29] A. Nellai Murugan and P. Iyadurai Selvaraj, Cycle & Armed Cap Cordial Graphs, International Journal of Mathematical Combinatorics, ISSN , Volume II, June 2016,pp
![[11] A.Nellai Murugan and J.Shiny Priyanka, Tree Related Extended Mean Cordial Graphs, International Journal of Research -Granthaalayah, ISSN 2350-0530,Vol.3, Issue 9,September. 2015, PP 143-148. I.F.](/docs-images/46/23537048/images/page_4.jpg "2.035(I2OR). [12] A.Nellai Murugan and S.Heerajohn, Cycle Related Mean Square Cordial Graphs, International Journal Of Research & Development Organization Journal of Mathematics,Vol.")
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