4 papers · 1 filter
A Unified Spectral Framework for Weighted Adjacency-Degree Matrices of Dendrimer and Bethe Trees
Metrose Metsidik
We introduce a weighted adjacency-degree matrix \(A_{fg}(G)\) with edge weights \(f(d_i,d_j)\) and diagonal entries \(g(d_i)\), unifying adjacency, Laplacian, signless Laplacian, \…
Eulerian and Bipartite Partial Duals of Hypermaps
Yufan Han, Metrose Metsidik
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 involu…
Two conjectures on graphs and their edge-path matrices
Metrose Metsidik, Xian'an Jin
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. [O…
Characterizations of bipartite and Eulerian partial duals of orientable hypermaps
Yufan Han, Metrose Metsidik
We first rewrite the Chmutov and Vignes-Tourneret's three-permutation formula as an explicit hyperedge-partial-duality formula in the two-permutation model, and show that in this m…