On edge irregularity strength of line graph and line cut-vertex graph of comb graph

H. M. Nagesh and V. R. Girish
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 28, 2022, Number 3, Pages 517–524
DOI: 10.7546/nntdm.2022.28.3.517-524
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Authors and affiliations

H. M. Nagesh
Department of Science & Humanities, PES University
Electronic City Campus, Hosur Road, Bangalore – 560 100, India

V. R. Girish
Department of Science & Humanities, PES University
Electronic City Campus, Hosur Road, Bangalore – 560 100, India

Abstract

For a simple graph G, a vertex labeling \phi:V(G) \rightarrow \{1, 2,\ldots,k\} is called k-labeling. The weight of an edge xy in G, written w_{\phi}(xy), is the sum of the labels of end vertices x and y, i.e., w_{\phi}(xy)=\phi(x)+\phi(y). A vertex k-labeling is defined to be an edge irregular k-labeling of the graph G if for every two different edges e and f, w_{\phi}(e) \neq w_{\phi}(f). The minimum k for which the graph G has an edge irregular k-labeling is called the edge irregularity strength of G, written es(G). In this paper, we find the exact value of edge irregularity strength of line graph of comb graph P_n \bigodot K_1 for n=2,3,4; and determine the bounds for n \geq 5. Also, the edge irregularity strength of line cut-vertex graph of P_n \bigodot K_1 for n=2; and determine the bounds for n \geq 3.

Keywords

  • Irregular assignment
  • Irregularity strength
  • Irregular total k-labeling
  • Edge irregularity strength
  • Comb graph

2020 Mathematics Subject Classification

  • 05C38
  • 05C78

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Manuscript history

  • Received: 4 March 2022
  • Revised: 2 August 2022
  • Accepted: 4 August 2022
  • Online First: 10 August 2022

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Cite this paper

Nagesh, H. M, & Girish, V. R. (2022). On edge irregularity strength of line graph and line cut-vertex graph of comb graph. Notes on Number Theory and Discrete Mathematics, 28(3), 517-524, DOI: 10.7546/nntdm.2022.28.3.517-524.

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