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Irregularity Strength of Regular Graphs [PDF]
The Electronic Journal of Combinatorics, 2008 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 $f:E(G)\rightarrow \{1,2,\ldots,w\}$. An irregularity strength of $G$, $s(G)$, is the smallest $w$ such that there is a $w$-weighting of $G$ for which $\sum_{e:u\in e}f(e)\neq\sum_{e:v\in e}f(e)$ for all pairs of
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The irregularity strength of circulant graphs
Discrete Mathematics, 2005 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Baril, Jean-Luc +2 more
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Journal of Natural Fibers, 2021 This study discussed the influence of fiber length distribution on yarn qualities (yarn irregularity and strength) based on simulation on fiber random arrangement.
Zhan Jiang +4 more
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Total vertex irregularity strength of trees with maximum degree five
Electronic Journal of Graph Theory and Applications, 2018 In 2010, Nurdin, Baskoro, Salman and Gaos conjectured that the total vertex irregularity strength of any tree T is determined only by the number of vertices of degrees 1, 2 and 3 in T. This paper will confirm this conjecture by considering all trees with
S. Susilawati +2 more
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The irregularity strength of tP3
Discrete Mathematics, 1991 The irregularity strength \(s(G)\) of a simple graph \(G\) is the smallest number such that the edges of \(G\) may be assigned weights \(\leq s(G)\) in such a way as to obtain distinct weight sums at each vertex. It is shown by elementary arguments in additive number theory that for \(G=tP_ 3\), the disjoint union of \(t\) paths of length 3, \([(15t-1)/
Kinch, Lael, Lehel, Jenő
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The Modular Irregularity Strength of C_n⊙mK_1
InPrime, 2022 Let G(V, E) be a graph with order n with no component of order 2. An edge k-labeling α: E(G) →{1,2,…,k} is called a modular irregular k-labeling of graph G if the corresponding modular weight function wt_ α:V(G) → Z_n defined by wt_ α(x) =Ʃ_(xyϵE(G)) α ...
Putu Kartika Dewi
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The irregularity strength of tKp
Discrete Mathematics, 1995 The irregularity strength of a simple graph is the smallest integer for which the edges may be assigned weights not exceeding it, such that the weight sums of adjacent edges are different at all vertices. A general formula is obtained for the irregularity strength of disjoint unions of identical complete graphs.
Jendroľ, Stanislav, Tkáč, Michal
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Irregularity strength of trees
Discrete Mathematics, 1998 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Amar, D., Togni, O.
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On irregularity strength of disjoint union of friendship graphs
Electronic Journal of Graph Theory and Applications, 2013 We investigate the vertex total and edge total modication of the well-known irregularity strength of graphs. We have determined the exact values of the total vertex irregularity strength and the total edge irregularity strength of a disjoint union of ...
Ali Ahmad, Martin Baca, Muhammad Numan
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Irregularity strength of digraphs
Discrete Mathematics, 2009 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ferrara, Mike +3 more
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