Shao, Zeling
Department of Mathematics, Hebei University of Technology, China

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The dispersability of the Kronecker cover of the product of complete graphs and cycles Shao, Zeling; Cui, Yaqin; Li, Zhiguo
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 12, No 1 (2024): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2024.12.1.10

Abstract

The Kronecker cover of a graph G is the Kronecker product of G and K2. The matching book embedding of a graph G is an embedding of G with the vertices on the spine, each edge within a single page so that the edges on each page do not intersect and the degree of vertices on each page is at most one. The matching book thickness of G is the minimum number of pages in a matching book embeddding of G and it denoted by mbt(G). A graph G is dispersable if mbt(G)=Δ(G), nearly dispersable if mbt(G)=Δ(G)+1. In this paper, the dispersability of the Kronecker cover of the Cartesian product of complete graphs Kp and cycles Cq is determined.
The Alon-Tarsi number of cupolarotundas and gyroelongated rotunda Li, Zhiguo; Gai, Yujia; Shao, Zeling
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 12, No 2 (2024): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2024.12.2.5

Abstract

The Alon-Tarsi number of a graph G is the smallest k so that there exists an orientation D of G with max outdegree k - 1 satisfying the number of even Eulerian subgraphs different from the number of odd Eulerian subgraphs. This paper is devoted to the study of the Alon-Tarsi number of cupolarotundas and gyroelongated rotunda.