𝔖 Bobbio Scriptorium
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Irregularity strength and compound graphs

✍ Scribed by Olivier Togni


Book ID
108316429
Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
116 KB
Volume
218
Category
Article
ISSN
0012-365X

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Irregularity strength of dense graphs
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## Abstract 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__) β†’ {1, 2,…, __w__}. For a vertex __v__, __f__(__v__) is defined as the sum __f__(__e__) over all edges

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## Abstract An assignment of positive integer weights to the edges of a simple graph __G__ is called irregular, if the weighted degrees of the vertices are all different. The irregularity strength, __s__(__G__), is the maximal weight, minimized over all irregular assignments. In this study, we show