# On infinite graphs and related matrices

 dc.contributor.author Ancykutty, Joseph dc.contributor.author Dr.Krishnamoorthy,A dc.contributor.author Dr.Thrivikraman, T dc.date.accessioned 2014-01-08T06:11:34Z dc.date.available 2014-01-08T06:11:34Z dc.date.issued 2000 dc.identifier.uri http://dyuthi.cusat.ac.in/purl/3142 dc.description Department of mathematics, Cochin University of Science and Technology en_US dc.description.abstract This thesis Entitled On Infinite graphs and related matrices.ln the last two decades (iraph theory has captured wide attraction as a Mathematical model for any system involving a binary relation. The theory is intimately related to many other branches of Mathematics including Matrix Theory Group theory. Probability. Topology and Combinatorics . and has applications in many other disciplines..Any sort of study on infinite graphs naturally involves an attempt to extend the well known results on the much familiar finite graphs. A graph is completely determined by either its adjacencies or its incidences. A matrix can convey this information completely. This makes a proper labelling of the vertices. edges and any other elements considered, an inevitable process. Many types of labelling of finite graphs as Cordial labelling, Egyptian labelling, Arithmetic labeling and Magical labelling are available in the literature. The number of matrices associated with a finite graph are too many For a study ofthis type to be exhaustive. A large number of theorems have been established by various authors for finite matrices. The extension of these results to infinite matrices associated with infinite graphs is neither obvious nor always possible due to convergence problems. In this thesis our attempt is to obtain theorems of a similar nature on infinite graphs and infinite matrices. We consider the three most commonly used matrices or operators, namely, the adjacency matrix en_US dc.description.sponsorship Cochin University of Science and Technology en_US dc.language.iso en en_US dc.publisher Cochin University of Science and Technology en_US dc.subject Graphs and Digraphs en_US dc.subject Theory of rings en_US dc.subject Adjacency matrix, en_US dc.subject Infinite digraph en_US dc.subject Arc adjacency operator en_US dc.title On infinite graphs and related matrices en_US dc.type Thesis en_US
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