 ﻿

# Math. J. Interdiscip. Sci. ### Duplicating a Vertex with an Edge in Divided Square Difference Cordial Graphs

A A Leo and R Vikramaprasad

• Download PDF
• DOI Number
https://doi.org/10.15415/mjis.2018.71001

## Volume 7, Number 1 (Sep-2018)

 KEYWORDS Duplication of a vertex by an edge, path, cycle graph, star graph, wheel graph, helm graph, crown graph, comb graph, snake graph. PUBLISHED DATE September 2018 PUBLISHER The Author(s) 2018. This article is published with open access at www.chitkara.edu.in/publications. ABSTRACT In this present work, we discuss divided square difference (DSD) cordial labeling in the context of duplicating a vertex with an edge in DSD cordial graphs such as path graph, cycle graph, star graph, wheel graph, helm graph, crown graph, comb graph and snake graph. INTRODUCTION By a graph, we mean a finite, undirected graph without loops and multiple edges. For basic definitions we refer (Harary 1969). In 1967, (Rosa, 1967) introduced a labeling of G called β-valuation. A dynamic survey on different graph labeling was found in Gallian (Gallian, 2008). Cordial labeling was introduced by (Cahit, 1987). (R. Varatharajan, 2011) have introduced the notion of divisor cordial labeling. (Alfred Leo, 2018) introduced divided square difference cordial labeling graphs. (Kaneria, 2016) introduced balanced cordial labeling. The motivation behind the divided square difference cordial labeling is due to R. Dhavaseelan et.al on their work even sum cordial labeling graphs (R. Dhavaseelan et. al, 2015). The motivation behind this article is due to S.K. Vaidya et.al on their work (S. K. Vaidya et. al, 2012). In this present work, we discuss divided square difference (DSD) cordial labeling in the context of duplication of a vertex by an edge in DSD cordial graphs such as path graph, cycle graph, star graph, wheel graph, helm graph, bistar graph, crown graph, comb graph and snake graph. Page(s) 1-8 URL http://dspace.chitkara.edu.in/jspui/bitstream/123456789/754/3/001_MJIS.pdf ISSN Print: 2278-9561, Online: 2278-957X DOI https://doi.org/10.15415/mjis.2018.71001 CONCLUSION In this article, we have discussed and proven that the graph got by duplicating a vertex with an edge in divided square difference (DSD) cordial graphs such as path graph, cycle graph, star graph, wheel graph, helm graph, bistar graph, crown graph, comb graph and snake graph were also DSD cordial graphs. REFERENCES Leo A. A., Vikramaprasad R. and Dhavaseelan R. (2018). Divided square difference cordial labeling graphs, International Journal of Mechanical Engineering and Technology, 9(1), 1137–1144. Leo A. A. and Vikramaprasad R. (2018). Divided square difference cordial labeling of some special graphs, International Journal of Engineering and Technology, 7(2), 935–938. Leo A. A. and Vikramaprasad R. (2018). More results on divided square difference cordial graphs, International Journal of Scientific Research and Review, 7(5), 380–385. Leo A. A. and Vikramaprasad R. (2018). Path related balanced divided square difference cordial graphs, International Journal of Computer Sciences and Engineering, 6(6), 727–731. Cahit I. (1987). “Cordial graphs: a weaker version of graceful and harmonious graphs,” Ars Combinatoria, 23, 201–207. Dhavaseelan R., Vikramaprasad R. and Abhirami S. (2015). A new notions of cordial labeling graphs, Global Journal of Pure and Applied Mathematics, 11(4), 1767–1774. Gallian J. A. (2008). A dynamic survey of graph labeling, Electronic J. Combin. 15, DS6,1–190. Harary F. (1969). Graph theory, Addison-Wesley, Reading, MA. Kaneria V. J., Patadiya Kalpesh M. and Jeydev R. (2016). Teraiya, Balanced cordial labeling and its applications to produce new cordial families, International Journal of Mathematics and its Applications, 4(1-C), 65–68. Rosa A. (1967). On certain valuations of the vertices of a graph, Theory of Graphs (International Symposium, Rome, July 1966), Gordon and Breach, N. Y. and Dunod Paris 349–355. Varatharajan R., Navaneethakrishnan S. and Nagarajan K. (2011). Divisor cordial graphs, International J. Math. Combin, 4, 15–25. Vaidya S. K. and Barasara C. M. (2012). Harmonic mean labeling in the context of duplication of graph elements, Elixir Discrete Mathematics, 48, 9482–9485. 