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Title
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Constructions of Ramanujan graphs from classes of regular graphs.
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Author
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Beach, Ross Joseph
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Abstract/Description
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In this paper, we are going to show the existence of Ramanujan graphs among different classes of graphs. The main areas of research surrounding these graphs consider their classification and existence for different degrees and orders. The focus of this body of work is to observe different classes of graphs, and to see if they fit the definition of Ramanujan graph under certain conditions. First, we examine whether all strongly regular graphs are Ramanujan. Then, different restrictions are...
Show moreIn this paper, we are going to show the existence of Ramanujan graphs among different classes of graphs. The main areas of research surrounding these graphs consider their classification and existence for different degrees and orders. The focus of this body of work is to observe different classes of graphs, and to see if they fit the definition of Ramanujan graph under certain conditions. First, we examine whether all strongly regular graphs are Ramanujan. Then, different restrictions are placed on the parameters of strongly regular graphs, and we explore whether those yield Ramanujan graphs. Some other results related to graph factors and some special graphs are observed as well.
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Identifier
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1298600893, WFE0000787
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Format
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Document (PDF)