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 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...
متن کاملNeighbor sum distinguishing edge colorings of graphs with small maximum average degree
A proper edge-k-coloring of a graph G is an assignment of k colors 1, 2, · · · , k to the edges of G such that no two adjacent edges receive the same color. A neighbor sum distinguishing edge-k-coloring of G is a proper edge-k-coloring of G such that for each edge uv ∈ E(G), the sum of colors taken on the edges incident with u is different from the sum of colors taken on the edges incident with...
متن کاملThe neighbour-sum-distinguishing edge-colouring game
Let γ : E(G) −→ N∗ be an edge colouring of a graph G and σγ : V (G) −→ N∗ the vertex colouring given by σγ(v) = ∑ e3v γ(e) for every v ∈ V (G). A neighbour-sumdistinguishing edge-colouring of G is an edge colouring γ such that for every edge uv in G, σγ(u) 6= σγ(v). The study of neighbour-sum-distinguishing edge-colouring of graphs was initiated by Karoński, Łuczak and Thomason [8]. They conjec...
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 $n$...
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ژورنال
عنوان ژورنال: Graphs and Combinatorics
سال: 2012
ISSN: 0911-0119,1435-5914
DOI: 10.1007/s00373-012-1191-x