Author

Metrose Metsidik

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Preprint Aug 2026

Two conjectures on graphs and their edge-path matrices

The edge-path matrix is a square matrix where each off-diagonal entry records the maximum number of edge-disjoint paths between the corresponding pair of vertices. Akbari et al. [On edge-path eigenvalues of graphs, Linear Multilinear Algebra 70 (2022) 2998-3008] proposed two conjectures: Conjecture 1 relates the edge-p...

Metrose Metsidik, Xian'an Jin · 0 citations

Preprint Sep 2026

Eulerian and Bipartite Partial Duals of Hypermaps

We study hyperedge partial duals of finite hypermaps in a purely combinatorial framework, without assuming orientability. A hypermap is represented by three fixed-point-free involutions $(\tau_0,\tau_1,\tau_2)$ on its flag set. We first give an explicit construction of the medial map from this model: $02$-orbits become...

Yu-Fan Han, Metrose Metsidik · 0 citations