Note on group irregularity strength of disconnected graphs
نویسندگان
چکیده
منابع مشابه
Group irregularity strength of connected graphs
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...
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Let G be a simple graph of order n with no isolated vertices and no isolated edges. For a positive integer w, an assignment f on G is a function f : E(G) → {1, 2, . . . , w}. For a vertex v, f(v) is defined as the sum f(e) over all edges e of G incident with v. f is called irregular, if all f(v) are distinct. The smallest w for which there exists an irregular assignment on G is called the irreg...
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Martin Bača et al. [2] introduced the problem of determining the total vertex irregularity strengths of graphs. In this paper we discuss how the addition of new edge affect the total vertex irregularity strength.
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Let G be a simple graph with no isolated edges and at most one isolated vertex. For a positive integer w, a w-weighting of G is a map f : E(G) → {1, 2, . . . , w}. An irregularity strength of G, s(G), is the smallest w such that there is a w-weighting of G for which ∑
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ژورنال
عنوان ژورنال: Open Mathematics
سال: 2018
ISSN: 2391-5455
DOI: 10.1515/math-2018-0017