International Journal of Mathematical Combinatorics, Vol.6

The International J.Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, sponsored by the MADIS of Chinese Academy of Sciences and published in USA quarterly comprising 460 pages approx. per volume, which publishes original research papers and survey articles in all aspects of Smarandache multi-spaces, Smarandache geometries, mathematical combinatorics, non-euclidean geometry and topology and their applications to other sciences

Some Topics of Special Interest in Graph Theory

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Some Investigations in the Theory of Graphs

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Discussion On Some Important Topics in Graph Theory

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The role of interior and closure operator in medical applications

In this paper, we consider the interior and closure operator as topological tools to apply in divisor cordial labeling. We investigate the properties related to the path with certain examples in a divisor cordial graphic topology. This concept is utilized in human blood circulation path and the results are analyzed.Publisher's Versio

Some Graph Laplacians and Variational Methods Applied to Partial Differential Equations on Graphs

In this dissertation we will be examining partial differential equations on graphs. We start by presenting some basic graph theory topics and graph Laplacians with some minor original results. We move on to computing original Jost graph Laplacians of friendly labelings of various finite graphs. We then continue on to a host of original variational problems on a finite graph. The first variational problem is an original basic minimization problem. Next, we use the Lagrange multiplier approach to the Kazdan-Warner equation on a finite graph, our original results generalize those of Dr. Grigor’yan, Dr. Yang, and Dr. Lin. Then we do an original saddle point approach to the Ahmad, Lazer, and Paul resonant problem on a finite graph. Finally, we tackle an original Schrödinger operator variational problem on a locally finite graph inspired by some papers written by Dr. Zhang and Dr. Pankov. The main keys to handling this difficult breakthrough Schrödinger problem on a locally finite graph are Dr. Costa’s definition of uniformly locally finite graph and the locally finite graph analog Dr. Zhang and Dr. Pankov’s compact embedding theorem when a coercive potential function is used in the energy functional. It should also be noted that Dr. Zhang and Dr. Pankov’s deeply insightful Palais-Smale and linking arguments are used to inspire the bulk of our original linking proof