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Quantifying Network Reliability Through Finding An Upper Bound For Graph Integrity Using Graph Coloring, Ian Burchett
Quantifying Network Reliability Through Finding An Upper Bound For Graph Integrity Using Graph Coloring, Ian Burchett
Mahurin Honors College Capstone Experience/Thesis Projects
Integrity of a graph is defined as 𝐺 = 𝑚𝑖𝑛𝑆⊆𝑉(𝐺){ 𝑆 + 𝑚 𝐺 − 𝑆 } , where G is a graph with vertex set V and m(G-S) denotes the order of the largest component of G - S. This provides an upper estimate of the integrity of the given graph. Using graph coloring, the color sequence of the graph can be generated, with the leading term being the largest component of the graph, the maximal independent set. The determination of the set is too time intensive to be feasible for moderate to large graphs, since there is no …