Distance three labelings of trees

Vertex Equitable Labelings of Transformed Trees

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...

Distance Constrained Labelings of Trees

An H(p, q)-labeling of a graph G is a vertex mapping f : VG → VH such that the distance (in the graph H) of f(u) and f(v) is at least p (at least q) if the vertices u and v are adjacent in G (are at distance two in G, respectively). This notion generalizes the notions of L(p, q)and C(p, q)-labelings of graphs studied as a graph model of the Frequency Assignment Problem. We study the computation...

Binary Labelings for Plane Quadrangulations and their Relatives

Motivated by the bijection between Schnyder labelings of a plane triangulation and partitions of its inner edges into three trees, we look for binary labelings for quadrangulations (whose edges can be partitioned into two trees). Our labeling resembles many of the properties of Schnyder’s one for triangulations: Apart from being in bijection with tree decompositions, paths in these trees allow ...

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 ...