# 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
Full paper (PDF, 172 Kb)

## Details

### 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 , a vertex labeling is called -labeling. The weight of an edge in , written , is the sum of the labels of end vertices and , i.e., . A vertex -labeling is defined to be an edge irregular -labeling of the graph if for every two different edges and , . The minimum for which the graph has an edge irregular -labeling is called the edge irregularity strength of , written . In this paper, we find the exact value of edge irregularity strength of line graph of comb graph for ; and determine the bounds for . Also, the edge irregularity strength of line cut-vertex graph of for ; and determine the bounds for .

### Keywords

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

• 05C38
• 05C78

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