A strong k-edge-coloring of a graph G is an assignment of k colors to the edges of G in such a way that any two edges meeting at a common vertex, or being adjacent to the same edge of G, are assignedâ€¦ (More)

Applying the recently obtained distributive lattice structure on the set of 1-factors, we show that the resonance graphs of any benzenoid systems G, as well as of general plane (weakly) elementaryâ€¦ (More)

Let D be a set of positive integers. The distance graph G(Z , D) with distance set D is the graph with vertex set Z in which two vertices x, y are adjacent if and only if |x âˆ’ y| âˆˆ D. The fractionalâ€¦ (More)

Let G = (V, E) be a (p, q)-graph. Let f : E â†’ {1, 2, . . . , q} be a bijection. The induced mapping f : V â†’ Zp of f is defined by f (u) â‰¡ âˆ‘ uvâˆˆE f(uv) (mod p) for u âˆˆ V . If f is a bijection, then Gâ€¦ (More)

Given two graphs G and H. The composition of G with H is the graph with vertex set V (G) Ã— V (H) in which (u1, v1) is adjacent to (u2, v2) if and only if u1u2 âˆˆ E(G) or u1 = u2 and v1v2 âˆˆ E(H). Inâ€¦ (More)

The generalized Mycielskians (also known as cones over graphs) are the natural generalization of the Mycielski graphs (which were first introduced by Mycielski in 1955). Given a graph G and anyâ€¦ (More)

Denote by Bâˆ— n the set of all kâˆ—-cycle resonant hexagonal chains with n hexagons. For any Bn âˆˆ B âˆ— n , let m(Bn) and i(Bn) be the numbers of matchings (=the Hosoya index) and the number ofâ€¦ (More)

Let G be a plane bipartite graph and M(G) the set of perfect matchings of G. The Z-transformation graph of G is defined as a graph on M(G): M,M â€² âˆˆ M(G) are joined by an edge if and only if theyâ€¦ (More)