Eigenvalue −1 of the Vertex Quadrangulation of a 4-Regular Graph
Vladimir R. Rosenfeld
Abstract:The vertex quadrangulation QG of a 4-regular graph G visually looks like a graph whose vertices are depicted as empty squares, and the connecting edges are attached to the corners of the squares. In a previous work [JOMC 59, 1551–1569 (2021)], the question was posed: does the spectrum of an arbitrary unweighted graph QG include the full spectrum {3,(−1)3} of the tetrahedron graph (complete graph K4)? Previously, many bipartite and nonbipartite graphs QG with such a subspectrum have been found; for example, a n… Show more
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