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Ancykutty, Joseph; Dr.Krishnamoorthy,A.
On *infinite* graphs and related matrices.

Degree: mathematics, 2000, Cochin University of Science and Technology

URL: http://dyuthi.cusat.ac.in/purl/3142

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

Cochin University of Science and Technology

Subjects/Keywords: Graphs and Digraphs; Theory of rings; Adjacency matrix,; Infinite digraph; Arc adjacency operator

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APA (6^{th} Edition):

Ancykutty, J. D. K. (2000). On infinite graphs and related matrices. (Thesis). Cochin University of Science and Technology. Retrieved from http://dyuthi.cusat.ac.in/purl/3142

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^{th} Edition):

Ancykutty, Joseph; Dr Krishnamoorthy,A. “On infinite graphs and related matrices.” 2000. Thesis, Cochin University of Science and Technology. Accessed October 20, 2019. http://dyuthi.cusat.ac.in/purl/3142.

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^{th} Edition):

Ancykutty, Joseph; Dr Krishnamoorthy,A. “On infinite graphs and related matrices.” 2000. Web. 20 Oct 2019.

Vancouver:

Ancykutty JDK. On infinite graphs and related matrices. [Internet] [Thesis]. Cochin University of Science and Technology; 2000. [cited 2019 Oct 20]. Available from: http://dyuthi.cusat.ac.in/purl/3142.

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Ancykutty JDK. On infinite graphs and related matrices. [Thesis]. Cochin University of Science and Technology; 2000. Available from: http://dyuthi.cusat.ac.in/purl/3142

Not specified: Masters Thesis or Doctoral Dissertation