As a natural extension of previously defined graph labelings, we introduce in this paper a new magic labeling whose evaluation is based on the neighbourhood of a vertex. We define a 1-vertex-magic… (More)

A 1-vertex-magic vertex labeling of a graph G(V,E) with p vertices is a bijection f from the vertex set V (G) to the integers 1, 2, . . . , p with the property that there is a constant k such that at… (More)

In this paper we introduce a new type of graph labeling, the (a, d)vertex-antimagic total labeling, which is a generalization of several other types of labelings. A connected graph G(V, E) is said to… (More)

A graph G is called edge-magic if there exists a bijection f : V (G) ∪ E(G) → {1, 2, 3, . . . , |V (G) ∪ E(G)|} such that f(x) + f(xy) + f(y) is a constant for every edge xy ∈ E(G). A graph G is said… (More)

A simple graph G = (V (G), E(G)) admits an H-covering, if every edge in E(G) belongs to at least one subgraph of G isomorphic to a given graph H. An (a, d)-H-antimagic total labeling of G admitting… (More)

The problem of determining the largest order nd,k of a graph of maximum degree at most d and diameter at most k is well known as the degree/diameter problem. It is known that nd,k Md,k where Md,k is… (More)

Let BCd,k be the largest possible number of vertices in a bipartite Cayley graph of degree d and diameter k. We show that BCd,k ≥ 2(k − 1)((d − 4)/3)k−1 for any d ≥ 6 and any even k ≥ 4, and BCd,k ≥… (More)