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http://hdl.handle.net/11375/6553
Title: | Almost Selfcomplementary Graphs and Extensions |
Authors: | Das, Kumar Pramod |
Advisor: | Rosa, Alexander |
Department: | Mathematics |
Keywords: | Mathematics;Mathematics |
Publication Date: | May-1989 |
Abstract: | <p>In this thesis the concept of selfcomplementary graphs is extended to almost selfcomplementary graphs. We dine a p-vertex graph to be almost selfcomplementary if it is isomorphic to its complement with respect to Kp-e, the complete graph with one edge deleted. An almost selfcomplementary graph with p vertices exists if and only if p=2 or 3 (mod 4), ie., precisely when selfcomplementary graphs do not exist. We investigate various properties of almost selfcomplementary graphs and examine the similarities and differences with those of selfcomplementary graphs.</p> <p>The concepts of selfcomplementary and almost selfcomplementary graphs are combined to define so-called k-selfcomplementary graphs which include the former two classes as subclasses. Although a k-selfcomplementary graph may contain fewer edges than a selfcomplementary or an almost selfcomplementary graph it is found that the former preserves most of the properties of the latter graphs.</p> <p>The notion of selfcomplementarity is further extended to combinatorial designs. In particular, we examine whether a Steiner triple system (twofold triple system, and a Steiner system S(2,4,v), respectively) can be partitioned into two isomorphic hypergraphs.</p> |
URI: | http://hdl.handle.net/11375/6553 |
Identifier: | opendissertations/1861 3040 1356834 |
Appears in Collections: | Open Access Dissertations and Theses |
Files in This Item:
File | Size | Format | |
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fulltext.pdf | 6.05 MB | Adobe PDF | View/Open |
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