The irregularity strength of circulant graphs
نویسندگان
چکیده
The irregularity strength of a simple graph is the smallest integer k for which there exists a weighting of the edges with positive integers at most k such that all the weighted degrees of the vertices are distinct. In this paper we study the irregularity strength of circulant graphs of degree 4. We find the exact value of the strength for a large family of circulant graphs. © 2005 Elsevier B.V. All rights reserved.
منابع مشابه
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We investigate the irregularity strength (s(G)) and total vertex irregularity strength (tvs(G)) of circulant graphs Cin(1, 2, . . . , k) and prove that tvs(Cin(1, 2, . . . , k)) = ⌈ n+2k 2k+1 ⌉ , while s(Cin(1, 2, . . . , k)) = ⌈ n+2k−1 2k ⌉ except if either n = 2k + 1 or if k is odd and n ≡ 2k + 1(mod4k), then s(Cin(1, 2, . . . , k)) = ⌈ n+2k−1 2k ⌉ + 1.
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ورودعنوان ژورنال:
- Discrete Mathematics
دوره 304 شماره
صفحات -
تاریخ انتشار 2005