7 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…
Introducing a vertex polynomial invariant for embedded graphs
Qi Yan, Qingying Deng, Metrose Metsidik
The ribbon group action extends geometric duality and Petrie duality by defining two embedded graphs as twisted duals precisely when they lie within the same orbit under this group…
Multiplicative and mining property for stability numbers of graphs
Metrose Metsidik, Lixiao Xiao
-vertex stability number , and -edge stability number is defined similarly by setting $X\su…
Eulerian-minors and a concise recursive characterization of 4-regular planar graphs
Metrose Metsidik, Qi Yan
An Eulerian-minor of an Eulerian graph is obtained from an Eulerian subgraph of the Eulerian graph by contraction. The Eulerian-minor operation preserves Eulerian properties of gra…