Volume 47 | Number 1 | Year 2017 | Article Id. IJMTT-V47P507 | DOI : https://doi.org/10.14445/22315373/IJMTT-V47P507
In this paper we investigate some new families of vertex prime graphs.We show that the graphs kayak paddle KP(k,m,l) , book graph θ(Cm)n,*Irregular book graph θ(C)n ,C3 snake S(C3,m) , *m-fold triangular snake S(C3,m,n), sunflower graph SF(1,n),*m-fold-petal sunflower graph SF(m,n),(Cn)k and *One point union of k cycles not of equal length (C)k has Vertex Prime label. The * indicates new families are discussed and shown tobe vertex prime. We introduce a new type of graph labeling called as L-cordial labeling and show that K1,n ,path Pn, Cn, S(C3,m) are families of L-cordial graphs.
[1]Bapat Mukund V. and Limaye N.B., Some families of E3-cordial graphs, Proceedings of the National conference on Graphs, combinatorics, Algorithm & application at Anandnagar, Krishnankoli, 25-29th Nov.2004.
[2]CahitI.,cordial graphs, A weaker version of graceful and harmonious graphs Ars combinatoria 23 (1987), 201-207.
[3]Cahit I. and Yilmaz R., E3-cordial graphs, ArsCombinatoria, 54 (2000), 119-127.
[4]T. Deretsky, S. M. Lee, and J. Mitchem, On vertex prime labelings of graphs, in Graph Theory, Combinatorics and Applications Vol. 1, J. Alavi, G. Chartrand,O. Oellerman, and A. Schwenk, eds., Proceedings 6th International Conference Theory and Applications of Graphs (Wiley, New York, 1991) 359-369.
[5]Gallian J.A., A dynamic survey of graph labellings, Electronic Journal of Combinatorics, DS6, (2015).
[6]G.V. Ghodsara and J.P.Jena ,prime cordial labeling of the graphs related to cycle with one chords, twin chordsand triangles.International journal of pure and applied mathematics Vol 89,no1,2013,79-87
[7] F.Harary Graph Theory,Narosa Publishing House ,New Delhi.
[9]J.Bhaskar Babuji and L.Shobana, prime and prime cordial labeling of some special graphs.,Int.J.cont .Math.Sciences,Vol 5,2010,no 47, 2347-2356
[10]M.Sundaram,R.ponrajand S.Somasundram,prime cordial labeling of graphs,Indian.Acad Math. 27,373-390(2005)
[11]S.K.Vaidya ,P.L.Vihol,prime cordial labeling of some graphs,Open journal of Discrete Mathematics,2,no1,(2012),11-16,doi:10.4236/ojdm.2012.21003
Mukund V.Bapat, "Some Vertex Prime Graphs And A New Type Of Graph Labeling," International Journal of Mathematics Trends and Technology (IJMTT), vol. 47, no. 1, pp. 49-55, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V47P507