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| Abstract: Graffiti.pc is a conjecture-making program written by Dr. Ermelinda DeLaViña. My senior project, which is advised by Dr. DeLaViña, is to resolve conjectures generated by Graffiti.pc. The conjectures are lower bounds of the independence number of the second power of connected cubic graphs. Independence number is the cardinality of a largest independence set; an independence set is a subset of the vertices where no two vertices of the subset are adjacent. An at most cubic graph is a simple graph in which the maximum degree is at most three. Let G be a simple graph. The second power of G is the graph on vertex set V(G) such that vertices v and u are adjacent if and only if they are at distance at most two. This presentation is the progress of my senior project, which consists of counterexamples and proofs for conjectures generated by Graffiti.pc. | ||||||
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