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Finding the Minimum Randic Index
Kunkler, Sarah Joyce
Kunkler, Sarah Joyce
Abstract
We show that finding a graph realization with the minimum Randic index for a given degree sequence is solvable in polynomial time. This is shown by reducing the problem to the minimum weight perfect b-matching problem. Using the b-matching problem, we find the realization with the minimum Randic index, but this graph is not guaranteed to be connected. In this case, we have developed a heuristic to connect the graph using two-switches, which preserves the degree sequence. From our experiments, the Randic index of the realization after our heuristic has a much lower percent difference from the minimum Randic index than that between the original and the minimum Randic index.
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Thesis is part of Honors ETD pilot project, 2008-2013. Migrated from Dspace in 2016.
Date
2012-07-13
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Keywords
Randic Index, Networks, Graphs, Graph Theory
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Mathematics