Z-transformation graphs of perfect matchings of hexagonal systems

71Citations
Citations of this article
5Readers
Mendeley users who have this article in their library.

Abstract

Let H be a hexagonal system. We define the Z-transformation graph Z(H) to be the graph where the vertices are the perfect matchings of H and where two perfect matchings are joined by an edge provided their symmetric difference is a hexagon of H. We prove that Z(H) is a connected bipartite graph if H has at least one perfect matching. Furthermore,Z(H) is either an elementary chain or graph with girth 4; and Z(H) - Vm is 2-connected, where Vm is the set of monovalency vertices in Z(H). Finally, we give those hexagonal systems whose Z-transformation graphs are not 2-connected. © 1988.

Cite

CITATION STYLE

APA

Fu-ji, Z., Xiao-feng, G., & Rong-si, C. (1988). Z-transformation graphs of perfect matchings of hexagonal systems. Discrete Mathematics, 72(1–3), 405–415. https://doi.org/10.1016/0012-365X(88)90233-6

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free