For an ordered subset W = {w1; w2; : : : ; wk} of vertices in a connected graph G and a vertex v of G, the metric representation of v with respect to W is the k-vector r(v |W ) = (d(v; w1), d(v; w2);â€¦ (More)

Expanding on a recent definition by Bialostocki and Voxman, we define the rainbow ramsey number RR(G1, G2) of two graphs G1 and G2 to be the minimum integer N such that any edge-coloring of theâ€¦ (More)

Let G and H be graphs. A graph with colored edges is said to be monochromatic if all its edges have the same color and rainbow if no two of its edges have the same color. Given two bipartite graphsâ€¦ (More)

Let G be a connected graph and S âŠ† V (G). Then the Steiner distance of S, denoted by dG(S), is the smallest number of edges in a connected subgraph of G containing S. Such a subgraph is necessarily aâ€¦ (More)

The metric dimension dim(G) of a graph G is the minimum number of vertices such that every vertex of G is uniquely determined by its vector of distances to the chosen vertices. The zero forcingâ€¦ (More)

Explicit formulae for the Î³-min and Î³-max labeling values of complete bipartite graphs are given, along with Î³-labelings which achieve these extremes. A recursive formula for the Î³-min labeling valueâ€¦ (More)

The notion of metric dimension, dim(G), of a graph G, as well as a number of variants, is now well studied. In this paper, we begin a local analysis of this notion by introducing cdimG(v), theâ€¦ (More)