A A Leo and R Vikramaprasad
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 βvaluation. 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)  18 
URL  http://dspace.chitkara.edu.in/jspui/bitstream/123456789/754/3/001_MJIS.pdf 
ISSN  Print: 22789561, Online: 2278957X 
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. 
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