Distance Constrained Labelings of Trees

Vertex Equitable Labelings of Transformed Trees

Distance constrained labelings of K4-minor free graphs

Motivated by previous results on distance constrained labelings and coloring of squares of K4-minor free graphs, we show that for every p ≥ q ≥ 1, there exists ∆0 such that every K4-minor free graph G with maximum degree ∆ ≥ ∆0 has an L(p, q)-labeling of span at most qb3∆(G)/2c. The obtained bound is the best possible.

Snakes and Caterpillars in Graceful Graphs

Graceful labelings use a prominent place among difference vertex labelings. In this work we present new families of graceful graphs all of them obtained applying a general substitution result. This substitution is applied here to replace some paths with some trees with a more complex structures. Two caterpillars with the same size are said to be textit{analogous} if thelarger stable sets, in bo...

Labeling trees with a condition at distance two

An L(h, k)-labeling of a graph G is an integer labeling of vertices of G, such that adjacent vertices have labels which differ by at least h, and vertices at distance two have labels which differ by at least k. The span of an L(h, k)-labeling is the difference between the largest and the smallest label. We investigate L(h, k)-labelings of trees of maximum degree ∆, seeking those with small span...

Exact Distance Labelings Yield Additive-Stretch Compact Routing Schemes

Distance labelings and compact routing schemes have both been active areas of recent research. It was already known that graphs with constant-sized recursive separators, such as trees, outerplanar graphs, series-parallel graphs and graphs of bounded treewidth, support both exact distance labelings and optimal (additive stretch 0, multiplicative stretch 1) compact routing schemes, but there are ...