Graphs which have n/2-minimal line-distinguishing colourings
نویسندگان
چکیده
منابع مشابه
Distinguishing graphs by edge-colourings
We investigate the distinguishing index D′(G) of a graph G as the least number d such that G has an edge-colouring with d colours that is only preserved by the trivial automorphism. This is an analog to the notion of the distinguishing number D(G) of a graph G, which is defined for colourings of vertices. We obtain a general upper bound D′(G) ≤ ∆(G) unless G is a small cycle C3, C4 or C5. We al...
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The Total Colouring Conjecture suggests that ∆ + 3 colours ought to suffice in order to provide a proper total colouring of every graph G with maximum degree ∆. Thus far this has been confirmed up to an additive constant factor, and the same holds even if one additionally requires every pair of neighbours in G to differ with respect to the sets of their incident colours, so called pallets. With...
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The vertex-distinguishing index χs(G) of a graph G is the minimum number of colours required to properly colour the edges of G in such a way that any two vertices are incident with different sets of colours. We consider this parameter for some regular graphs. Moreover, we prove that for any graph, the value of this invariant is not changed if the colouring above is, in addition, required to be ...
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Consider a simple graph G = (V,E) and its proper edge colouring c with the elements of the set {1, 2, . . . , k}. The colouring c is said to be neighbour sum distinguishing if for every pair of vertices u, v adjacent in G, the sum of colours of the edges incident with u is distinct from the corresponding sum for v. The smallest integer k for which such colouring exists is known as the neighbour...
متن کاملNeighbour-Distinguishing Edge Colourings of Random Regular Graphs
A proper edge colouring of a graph is neighbour-distinguishing if for all pairs of adjacent vertices v, w the set of colours appearing on the edges incident with v is not equal to the set of colours appearing on the edges incident with w. Let ndi(G) be the least number of colours required for a proper neighbour-distinguishing edge colouring of G. We prove that for d ≥ 4, a random d-regular grap...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1996
ISSN: 0012-365X
DOI: 10.1016/0012-365x(94)00365-p