4 papers
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…