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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.
Abstract: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. | ||||||