The Resonance Graphs Of Two Classes Of Hexagonal Systems On M(?)bius Strips

Hexagonal systems are 2-connected plane bipartite graphs with every inner face a hexagon and their resonance graphs reflect the structure of their perfect matchings. Fibonacenes are a class of hexagonal systems. In 2015, S. Klavzar and P. Zigert Pletersek have proved that the resonance graph of an arbitrary fibonacene with n hexagons is isomorphic to the Fibonacci cube Γ(?)In this paper, we consider the resonance graph of the fibonacenes with n hexagons on the M?bius strips and prove that:it is isomorphic to the union of An and two isolated vertices if n is odd, and the Lucas cube An if n is even. Futhermore, we show that the resonance graph of a class of hexagonal chain on the M?bius strip is isomorphic to the union of a subgraph of the hypercube Qn and two isolated vertices.