Friday, September 16, 2022 - 10:00 to 11:00
SCHOOL OF COMPUTER SCIENCE
The School of Computer Science is pleased to present…
MSc Thesis Proposal by: Daniel John
Date: Friday September 16th, 2022
Zoom Meeting URL: https://us06web.zoom.us/j/82293987196?from=addon
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A graph is a structure consisting of a set of vertices and edges. Graph construction has been a focus of research for a long time, and generating graphs has proven helpful in complex networks and artificial intelligence.
A significant problem that has been a focus of research is whether a given sequence of integers d1, d2,…, dn is graphical. Havel and Hakimi have stated necessary and sufficient conditions for a degree sequence to be graphic with different properties such as multigraphs without loops, connected, connected non-separable, and connected separable graphs. In our work, we have proved the sufficiency of the requirements by generating algorithms and providing constructive proof.
For a degree sequence, there might exist a realization with k-factors, and the k-factors of a graph can be connected and non-connected. This thesis explores determining if a degree sequence has at least one realization with a connected k-factor and identifying the sequences without any realization of the graph with connected k-factors. We also discuss the methods to generate graphic sequences which can realize graphs with connected k-factors.
Keywords: Graphical degree sequence, k-factor, graph generation
MSc Thesis Committee:
Internal Reader: Dr. Ahmad Biniaz
External Reader: Dr. Mehdi Sangani Monfared
Advisor: Dr. Asish Mukhopadhyay
MSc Thesis Proposal Announcement
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