Here, we demonstrate the promising tunneling property of electrons across quasi-graphene/poly(vinylidene fluoride) (PVDF) through the Coulomb blockade region. The melt-mixing technique is used to prepare such a nanocomposite by mixing a nanofiller into the polymer matrix. The structure and surface morphology are studied using X-ray diffraction and field-emission scanning electron microscopy measurements, which show defects oriented in the sample while the binding of matrix with the nanofiller remains highly conductive even upon its binding with the insulating matrix. Tunneling properties of quasi-graphene/PVDF are studied using scanning tunneling microscopy measurements, which indicate high resistance in the Coulomb blockade region. Potential aspects of quasi-graphene/PVDF as a flexible material for device applications are also discussed.

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Let G be a graph. The gamma graph of G denoted by γ ⋅ G is the graph with vertex set V(γ ⋅ G) as the set of all γ-sets of G and two vertices D and S of γ ⋅ G are adjacent if and only if |D ∩ S| = γ(G) – 1. A graph H is said to be a γ-graph if there exists a graph G such that γ ⋅ G is isomorphic to H. In this paper, we show that every induced subgraph of a γ-graph is also a γ-graph. Furthermore, if we prove that H is a γ-graph, then there exists a sequence {Gn} of non-isomorphic graphs such that H = γ ⋅ Gn for every n.