scholarly journals Asymptotic confirmation of the Faudree–Lehel conjecture on irregularity strength for all but extreme degrees

2021 ◽  
Author(s):  
Jakub Przybyło
Keyword(s):  
Irregularity Strength

scholarly journals The Irregularity and Modular Irregularity Strength of Fan Graphs

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 605
Author(s):  
Martin Bača ◽  
Zuzana Kimáková ◽  
Marcela Lascsáková ◽  
Andrea Semaničová-Feňovčíková
Keyword(s):  
Simple Graph ◽  
Isolated Vertex ◽  
Positive Integers ◽  
Irregularity Strength

For a simple graph G with no isolated edges and at most, one isolated vertex, a labeling φ:E(G)→{1,2,…,k} of positive integers to the edges of G is called irregular if the weights of the vertices, defined as wtφ(v)=∑u∈N(v)φ(uv), are all different. The irregularity strength of a graph G is known as the maximal integer k, minimized over all irregular labelings, and is set to ∞ if no such labeling exists. In this paper, we determine the exact value of the irregularity strength and the modular irregularity strength of fan graphs.

scholarly journals An iterative approach to graph irregularity strength

2010 ◽  
Vol 158 (11) ◽  
pp. 1189-1194 ◽  
Author(s):  
Michael Ferrara ◽  
Ronald Gould ◽  
Michał Karoński ◽  
Florian Pfender
Keyword(s):  
Iterative Approach ◽  
Irregularity Strength

On H-irregularity strength of cycles and diamond graphs

2021 ◽  
pp. 2150157
Author(s):  
Hayat Labane ◽  
Isma Bouchemakh ◽  
Andrea Semaničová-Feňovčíková
Keyword(s):  
Simple Graph ◽  
Strength Formula ◽  
Irregularity Strength

A simple graph [Formula: see text] admits an [Formula: see text]-covering if every edge in [Formula: see text] belongs to at least one subgraph of [Formula: see text] isomorphic to a given graph [Formula: see text]. The graph [Formula: see text] admits an [Formula: see text]-irregular total[Formula: see text]-labeling [Formula: see text] if [Formula: see text] admits an [Formula: see text]-covering and for every two different subgraphs [Formula: see text] and [Formula: see text] isomorphic to [Formula: see text], there is [Formula: see text], where [Formula: see text] is the associated [Formula: see text]-weight. The total[Formula: see text]-irregularity strength of [Formula: see text] is [Formula: see text]. In this paper, we give the exact values of [Formula: see text], where [Formula: see text]. For the versions edge and vertex [Formula: see text]-irregularity strength [Formula: see text] and [Formula: see text], respectively, we determine the exact values of [Formula: see text], [Formula: see text] and [Formula: see text], where [Formula: see text] is the diamond graph.

scholarly journals On the total H-irregularity strength of graphs: A new notion

2017 ◽  
Vol 855 ◽  
pp. 012004 ◽  
Author(s):  
Ika Hesti Agustin ◽  
Dafik ◽  
Marsidi ◽  
Ermita Rizki Albirri
Keyword(s):  
Irregularity Strength
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