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...
متن کاملDistinguishing number and distinguishing index of natural and fractional powers of graphs
The distinguishing number (resp. index) $D(G)$ ($D'(G)$) of a graph $G$ is the least integer $d$ such that $G$ has an vertex labeling (resp. edge labeling) with $d$ labels that is preserved only by a trivial automorphism. For any $n in mathbb{N}$, the $n$-subdivision of $G$ is a simple graph $G^{frac{1}{n}}$ which is constructed by replacing each edge of $G$ with a path of length $n$...
متن کاملDistant Set Distinguishing Total Colourings of Graphs
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...
متن کاملThe Distinguishing Index of Infinite Graphs
The distinguishing index D′(G) of a graph G is the least cardinal d such that G has an edge colouring with d colours that is only preserved by the trivial automorphism. This is similar to the notion of the distinguishing number D(G) of a graph G, which is defined with respect to vertex colourings. We derive several bounds for infinite graphs, in particular, we prove the general bound D′(G) 6 ∆(...
متن کاملOn Neighbor-Distinguishing Index of Planar Graphs
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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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2017
ISSN: 0012-365X
DOI: 10.1016/j.disc.2017.05.009