On total irregularity strength of caterpillar graphs with two leaves on each internal vertex

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.

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Computing the total edge irregularity strength for quintet snake graph and related graphs

Journal of Discrete Mathematical Sciences and Cryptography ◽

10.1080/09720529.2021.1878627 ◽

2021 ◽

pp. 1-14

Author(s):

F. Salama

Keyword(s):

Irregularity Strength ◽

Total Edge Irregularity Strength

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Total edge irregularity strength of (n,t)-kite graph

Journal of Physics Conference Series ◽

10.1088/1742-6596/1008/1/012049 ◽

2018 ◽

Vol 1008 ◽

pp. 012049 ◽

Cited By ~ 3

Author(s):

Tri Winarsih ◽

Diari Indriati

Keyword(s):

Irregularity Strength ◽

Total Edge Irregularity Strength

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An iterative approach to graph irregularity strength

Discrete Applied Mathematics ◽

10.1016/j.dam.2010.02.003 ◽

2010 ◽

Vol 158 (11) ◽

pp. 1189-1194 ◽

Cited By ~ 5

Author(s):

Michael Ferrara ◽

Ronald Gould ◽

Michał Karoński ◽

Florian Pfender

Keyword(s):

Iterative Approach ◽

Irregularity Strength

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On H-irregularity strength of cycles and diamond graphs

Discrete Mathematics Algorithms and Applications ◽

10.1142/s1793830921501573 ◽

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.

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