An improved upper bound for the neighbor sum distinguishing index of graphs
نویسندگان
چکیده
منابع مشابه
On the Neighbor Sum Distinguishing Index of Planar Graphs
Let c be a proper edge colouring of a graph G = (V,E) with integers 1, 2, . . . , k. Then k ≥ ∆(G), while by Vizing’s theorem, no more than k = ∆(G)+ 1 is necessary for constructing such c. On the course of investigating irregularities in graphs, it has beenmoreover conjectured that only slightly larger k, i.e., k = ∆(G) + 2 enables enforcing additional strong feature of c, namely that it attri...
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A proper edge colouring of a graph G without isolated edges is neighbour-distinguishing if any two adjacent vertices have distinct sets consisting of colours of their incident edges. The neighbour-distinguishing index of G is the minimum number ndi(G) of colours in a neighbour-distinguishing edge colouring of G. According to a conjecture by Zhang, Liu and Wang (2002), ndi(G) ≤ ∆(G) + 2 provided...
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AnL(2, 1)-labeling of a graphG is defined as a function f from the vertex setV (G) into the nonnegative integers such that for any two vertices x, y, |f (x)−f (y)| ≥ 2 if d(x, y) = 1 and |f (x)− f (y)| ≥ 1 if d(x, y) = 2, where d(x, y) is the distance between x and y in G. The L(2, 1)-labeling number λ2,1(G) of G is the smallest number k such that G has an L(2, 1)-labeling with k = max{f (x)|x ...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2014
ISSN: 0166-218X
DOI: 10.1016/j.dam.2014.05.013