On Neighbor-Distinguishing Index of Planar Graphs
نویسندگان
چکیده
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 that G is a connected graph of order at least 6. The conjecture is proved for planar graphs G with ∆(G) ≥ 12.
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ورودعنوان ژورنال:
- Journal of Graph Theory
دوره 76 شماره
صفحات -
تاریخ انتشار 2014