Sign Invertibility of Graphs

Abstract: A graph is considered invertible if its adjacency matrix representation is also invertible. While the process of finding invertible graphs is fairly simple, we can also study a subfamily of invertible graphs that are sign-invertible. For our research, a graph is considered sign-invertible if its graph’s adjacency matrix is invertible and its inverse is a matrix with each entry belonging to {−1, 0, 1}. While the idea of sign-invertibility was first introduced in the 1980s by Bucky, Doty and Harary, there has been little progress toward finding a complete categorization of sign invertible graphs since then, until Kalita and Sarma studied a sub-family of unicyclic graphs. We provided a complete categorization of both invertible and s-invertible graphs with at most two cycles and a partial characterization of sign-invertible cactus graphs.

computational geometrydiscrete mathematicscommutative algebracombinatorics

Audience: researchers in the topic

Copenhagen-Jerusalem Combinatorics Seminar

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