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178 papers · 1 filter
Hermitian adjacency matrices with at most three distinct eigenvalues
Saieed Akbari, Jonathan Aloni, Maxwell Levit +2
We study oriented graphs whose Hermitian adjacency matrices of the second kind have few eigenvalues. We give a complete characterization of the oriented graphs with two distinct ei…
Differential transcendence and walks on self-similar graphs
Yakob Kahane, Marni Mishna
Symmetrically self-similar graphs are an important type of fractal graph. Their Green functions satisfy order one iterative functional equations. We show when the branching number…
Guarding isometric subgraphs and Cops and Robber in planar graphs
Sebastián González Hermosillo de la Maza, Bojan Mohar
In the game of Cops and Robbers, one of the most useful results is that an isometric path in a graph can be guarded by one cop. In this paper, we introduce the concept of wide shad…
Centrality of star and monotone factorisations
Jesse Campion Loth, Amarpreet Rattan
A factorisation problem in the symmetric group is central if conjugate permutations always have the same number of factorisations. We give the first fully combinatorial proof of th…
Constructing cospectral graphs by unfolding non-bipartite graphs
M. Rajesh Kannan, Shivaramakrishna Pragada, Hitesh Wankhede
In 2010, Butler introduced the unfolding operation on a bipartite graph to produce two bipartite graphs, which are cospectral for the adjacency and the normalized Laplacian matrice…
Inhomogeneous order 1 iterative functional equations with applications to combinatorics
Lucia Di Vizio, Gwladys Fernandes, Marni Mishna
We show that if a Laurent series satisfies a particular kind of linear iterative equation, then is either a rational function or it is differentially tran…