Group irregularity strength of connected graphs
نویسندگان
چکیده
We investigate the group irregularity strength (sg(G)) of graphs, that is, we find the minimum value of s such that for any Abelian group G of order s, there exists a function f : E(G) → G such that the sums of edge labels at every vertex are distinct. We prove that for any connected graph G of order at least 3, sg(G) = n if n = 4k + 2 and sg(G) ≤ n + 1 otherwise, except the case of an infinite family of stars. We also prove that the presented labelling algorithm is linear with respect to the
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ورودعنوان ژورنال:
- J. Comb. Optim.
دوره 30 شماره
صفحات -
تاریخ انتشار 2015