Bounds for the Real Number Graph Labellings and Application to Labellings of the Triangular Lattice
نویسندگان
چکیده
We establish new lower and upper bounds for the real number graph labelling problem. As an application, we completely determine the optimum spans of L(p, q)-labellings of the infinite triangular plane lattice (solving an open problem of Griggs).
منابع مشابه
Triangular embeddings of complete graphs from graceful labellings of paths
We show that to each graceful labelling of a path on 2s + 1 vertices, s ≥ 2, there corresponds a current assignment on a 3-valent graph which generates at least 22s cyclic oriented triangular embeddings of a complete graph on 12s + 7 vertices. We also show that in this correspondence, two distinct graceful labellings never give isomorphic oriented embeddings. Since the number of graceful labell...
متن کاملRelaxed Graceful Labellings of Trees
A graph G on m edges is considered graceful if there is a labelling f of the vertices of G with distinct integers in the set {0, 1, . . . ,m} such that the induced edge labelling g defined by g(uv) = |f(u) − f(v)| is a bijection to {1, . . . ,m}. We here consider some relaxations of these conditions as applied to tree labellings: 1. Edge-relaxed graceful labellings, in which repeated edge label...
متن کاملConnections between labellings of trees
There are many long-standing conjectures related with some labellings of trees. It is important to connect labellings that are related with conjectures. We find some connections between known labellings of simple graphs.
متن کاملReal Number Channel Assignments for Lattices
We consider the problem of assigning a numerical channel to each transmitter in a large regular array such that multiple levels of interference, which depend on the distance between transmitters, are avoided by sufficiently separating the channels. The goal is to find assignments that minimize the span of the labels used. A previous paper of the authors introduced a model for this problem using...
متن کاملRecent progress in mathematics and engineering on optimal graph labellings with distance conditions
The problem of radio channel assignments with multiple levels of interference can be modelled using graph theory. The theory of integer vertex-labellings of graphs with distance conditions has been investigated for several years now, and the authors recently introduced a new model of real number labellings that is giving deeper insight into the problems. Here we present an overview of the recen...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- SIAM J. Discrete Math.
دوره 22 شماره
صفحات -
تاریخ انتشار 2008