منابع مشابه
On irregular total labellings
Two new graph characteristics, the total vertex irregularity strength and the total edge irregularity strength, are introduced. Estimations on these parameters are obtained. For some families of graphs the precise values of these parameters are proved. © 2006 Elsevier B.V. All rights reserved.
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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 کاملList version of ($p$,1)-total labellings
The (p,1)-total number λp (G) of a graph G is the width of the smallest range of integers that suffices to label the vertices and the edges of G such that no two adjacent vertices have the same label, no two incident edges have the same label and the difference between the labels of a vertex and its incident edges is at least p. In this paper we consider the list version. Let L(x) be a list of ...
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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...
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ژورنال
عنوان ژورنال: Tamkang Journal of Mathematics
سال: 2010
ISSN: 2073-9826,0049-2930
DOI: 10.5556/j.tkjm.41.2010.788