Analytic Approach to Study Hk Cordial Labeling of Graphs

Abstract

Graph theory is one of the prosperous branches of mathematics with widespread applications newlineto combinational and arithmetic aspects. The thought of graph theory can be used to newlineform various mathematical models for applied applications in Operation Research, Management, newlineEngineering; specially in research areas of computer science such as data mining, image newlinesegmentation, clustering, image capturing, networking which is used in structural models etc. newlineThese structural arrangements of different objects or tools lead to new modifications and inventions newlinein the existing situation for development in those fields. newlineMany real life problems can be modeled and converted into graph theoretical problems and newlinethen tried for solution. The concepts of graph theory can also be used in medical science to newlinestudy the structures of DNA and RNA. Electricity cable network, water cannel network and newlineGoogle map are well-known applications of graph theory. newlineThe concept of graph labeling is the interesting field of research in the current area for many newlineresearchers. A labeling of a graph G=(V;E) is a mapping that carries vertices, edges or both to newlinethe set of labels (usually to the positive or non-negative integers). At present various graph labeling newlinetechniques are available such as graceful, harmonious, prime, cordial, geometric, mean, newlinemagic type, square sum, permutation and combination etc. The interest in the field of graph newlinelabeling is constantly increasing and it has motivated many researchers. Graph labeling has newlineapplications in diversified fields such as coding theory, cryptography, X-ray crystallography, newlinecircuit design, astronomy and communication networks design. newlineIn this synopsis, and later in the thesis, the graphs considered are simple, finite, undirected newlineand connected. G = (V;E) denotes a graph with vertex set V and edge set E. p and q denote newlineorder and size of the graph respectively. We have mainly focused upon the graph families which newlinesatisfy the conditions of weaker versions of cordial labeling such as H-cordial, Hk-cordial and newlinesemi Hk-co