A d-dimensional hypercube drawing of a graph represents the vertices by distinct points in {0, 1}d, such that the line-segments representing the edges do not cross. We study lower and upper bounds on the minimum number of dimensions in hypercube drawing of a given graph. This parameter turns out to be related to Sidon sets and antimagic injections.

Suppose a graph G = (V, E) is simple, connected and finite with vertex set V(G) an edge E(G). The local antimagic coloring combination of labelling coloring. A mapping f∶ V (G)→ {1, 2, ..., |V (G)|} called if every two incident edges e_1and e_2, then the weights e_2 maynot be same, w(e_1) ≠ w(e_2), e uv ∈ G, w(e) f(u)+ f(v) rule that are colored according to their weights, w_e. Local has develo...

let g(v,e) be a graph with p vertices and q edges. a graph g is said to have an odd mean labeling if there exists a function f : v (g) → {0, 1, 2,...,2q - 1} satisfying f is 1 - 1 and the induced map f* : e(g) → {1, 3, 5,...,2q - 1} defined by f*(uv) = (f(u) + f(v))/2 if f(u) + f(v) is evenf*(uv) = (f(u) + f(v) + 1)/2 if f(u) + f(v) is odd is a bijection. a graph that admits an odd mean lab...

The study of graph labellings has focused on finding classes of graphs which admit a particular type of labelling. Here we consider variations of the well-known edge-magic and vertex-magic total labellings for which all graphs admit such a labelling. In particular, we consider two types of injections of the vertices and edges of a graph with positive integers: (1) for every edge the sum of its ...

Let be a simple, finite, connected, plane graph with the vertex set src=image/13427481_02.gif>, edge src=image/13427481_03.gif> and face src=image/13427481_04.gif>). Martin Baca [1] defined, connected src=image/13427481_04.gif> to src=image/13427481_05.gif> antimagic if there exists positive integers src=image/13427481_06.gif> src=image/13427481_07.gif> bijection...