منابع مشابه
Edge colouring by total labellings
We introduce the concept of an edge-colouring total k-labelling. This is a labelling of the vertices and the edges of a graph G with labels 1, 2, . . . , k such that the weights of the edges define a proper edge colouring of G. Here the weight of an edge is the sum of its label and the labels of its two endvertices. We define χt(G) to be the smallest integer k for which G has an edge-colouring ...
متن کاملEdge-colouring and total-colouring chordless graphs
A graph G is chordless if no cycle in G has a chord. In the present work we investigate the chromatic index and total chromatic number of chordless graphs. We describe a known decomposition result for chordless graphs and use it to establish that every chordless graph of maximum degree ∆ ≥ 3 has chromatic index ∆ and total chromatic number ∆+1. The proofs are algorithmic in the sense that we ac...
متن کاملGeneralized edge-magic total labellings of models from researching networks
Graph labellings have been used in many applications, such as in the development of redundant arrays of independent disks which incorporate redundancy utilizing erasure codes, some algorithms, design of highly accurate optical gauging systems for use on automatic drilling machines, design of angular synchronization codes, design of optimal component layouts for certain circuit-board geometries,...
متن کاملEdge irregular total labellings for graphs of linear size
Confirming a conjecture by Ivančo and Jendrol’ for a large class of graphs we prove that for every graph G = (V,E) of order n, size m and maximum degree ∆ with m > 111000∆ there is a function f : V ∪ E → { 1, 2, ..., ⌈ m+2 3 ⌉} such that f(u) + f(uv) + f(v) 6= f(u′) + f(u′v′) + f(v′) for every uv, u′v′ ∈ E with uv 6= u′v′. Furthermore, we prove the existence of such a function with values up to...
متن کاملEdge-Injective and Edge-Surjective Vertex Labellings
For a graph G = (V,E) we consider vertex-k-labellings f : V → {1, 2, . . . , k} for which the induced edge weighting w : E → {2, 3, . . . , 2k} with w(uv) = f(u) + f(v) is injective or surjective or both. We study the relation between these labellings and the number theoretic notions of an additive basis and a Sidon set, present a new construction for a so-called restricted additive basis and d...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2010
ISSN: 0012-365X
DOI: 10.1016/j.disc.2008.09.013