<abstract xmlns="http://www.w3.org/1999/xhtml">

A simple undirected graph = (<italic>V</italic> Γ<italic>, E</italic>Γ) admits an <italic>H</italic>-covering if every edge in <italic>E</italic> belongs to at least one subgraph of that is isomorphic to a graph <italic>H</italic>. For any graph admitting <italic>H</italic>-covering, a total labelling <italic>β : V</italic>Γ ∪<italic>E</italic>Γ→{1, 2<italic>, …, p</italic>} is called an <italic>H</italic>-irregular total <italic>p</italic>-labelling of Γ if every two different subgraphs <italic>H</italic>1 and <italic>H</italic>2 of isomorphic to <italic>H</italic> have distinct weights where the weight <italic>wβ</italic>(<italic>K</italic>) of subgraph <italic>K</italic> of Γ is defined as <inline-formula>
<alternatives>
<inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_auom-2023-0026_eq_001.png"></inline-graphic>
<math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>w</mi></mrow><mi>f</mi></msub><mrow><mo>(</mo><mi>K</mi><mo>)</mo></mrow><mo>:</mo><mo>=</mo><munder><mo>∑</mo><mrow><mi>v</mi><mo>∈</mo><msub><mrow><mi>V</mi></mrow><mi>K</mi></msub></mrow></munder><mrow><mi>f</mi><mrow><mo>(</mo><mi>v</mi><mo>)</mo></mrow><mo>+</mo><munder><mo>∑</mo><mrow><mi>e</mi><mo>∈</mo><msub><mrow><mi>E</mi></mrow><mi>K</mi></msub></mrow></munder><mrow><mi>f</mi><mrow><mo>(</mo><mi>e</mi><mo>)</mo></mrow></mrow></mrow></mrow></math>
<tex-math>{w_f}\left( K \right): = \sum\limits_{v \in {V_K}} {f\left( v \right) + \sum\limits_{e \in {E_K}} {f\left( e \right)} } </tex-math>
</alternatives>
</inline-formula>. The smallest number <italic>p</italic> for which a graph admits an <italic>H</italic>-irregular total <italic>p</italic>-labelling is called the total <italic>H-</italic>irregularity strength of Γ and is denoted by <italic>ths</italic>(Γ). In this paper, we determine the total <italic>H</italic>-irregularity strength of edge comb product of two graphs.
</abstract>

A simple undirected graph = (V Γ, EΓ) admits an H-covering if every edge in E belongs to at least one subgraph of that is isomorphic to a graph H. For any graph admitting H-covering, a total labelling β : VΓ ∪EΓ→{1, 2, …, p} is called an H-irregular total p-labelling of Γ if every two different subgraphs H1 and H2 of isomorphic to H have distinct weights where the weight wβ(K) of subgraph K of Γ is defined as 


wf(K):=∑v∈VKf(v)+∑e∈EKf(e)
{w_f}\left( K \right): = \sum\limits_{v \in {V_K}} {f\left( v \right) + \sum\limits_{e \in {E_K}} {f\left( e \right)} } 

. The smallest number p for which a graph admits an H-irregular total p-labelling is called the total H-irregularity strength of Γ and is denoted by ths(Γ). In this paper, we determine the total H-irregularity strength of edge comb product of two graphs.

Computing the total H-irregularity strength of edge comb product of graphs

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"Computing the total H-irregularity strength of edge comb product of graphs"}

A simple undirected graph = (V Γ, EΓ) admits an H-covering if every edge in E belongs to at least one subgraph of that is isomorphic to a graph H. For any...

Computing the total H-irregularity strength of edge comb product of graphs

Published Online: Mar 27, 2023

Page range: 177 - 189

Received: Aug 24, 2022

Accepted: Dec 28, 2022

DOI: https://doi.org/10.2478/auom-2023-0026

Keywords
Total -Irregular Strength, Edge Comb Product Graph, Cycle, Path

© 2023 Mohamad Fahruli Wahyujati et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Computing the total H-irregularity strength of edge comb product of graphs

Published Online: Mar 27, 2023

Page range: 177 - 189

Received: Aug 24, 2022

Accepted: Dec 28, 2022

DOI: https://doi.org/10.2478/auom-2023-0026

KeywordsTotal -Irregular Strength, Edge Comb Product Graph, Cycle, Path

© 2023 Mohamad Fahruli Wahyujati et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
Total -Irregular Strength, Edge Comb Product Graph, Cycle, Path