Further Results on (a, d) -total Edge Irregularity Strength of Graphs

Authors

Muthugurupackiam K., Department of Mathematics, Government Arts and Science College, Srivilliputtur – 626 125, Tamil Nadu, India.Follow
Pandiaraj P., Department of Mathematics, Kamaraj College of Engineering and Technology, Madurai - 625 701, Tamil Nadu, India / Rajah Serfoji Government College, Bharathidasan University, Tiruchirappalli, Tamil Nadu, India.Follow
Gurusamy R., Department of Mathematics, Mepco Schlenk Engineering College, Sivakasi - 626 005, Tamil Nadu, India.Follow
Muthuselvam I., Department of Mathematics, Kalasalingam Academy of Research and Education, Krishnankoil – 626 126, Tamil Nadu, India.Follow

Abstract

Consider a simple graph ��=(��,��)on��vertices and ��edges together with a total ℎ–labeling ��:��(��)∪��(��)→{1,2,3,...,ℎ}. Then ρ is called (��,��)–total edge irregular labeling if there exists a one-to-one correspondence, say ��:��(��)→{��,��+��,��+2��,...+��+(��−1)��}defined by ��(����)=��(��)+��(��)+��(����)for all ����∈��(��),where ��≥3,��≥2.Also, the value ��(����)is said to be the edge weight of ����. The (��,��)−total edge irregularity strength of the graph G is indicated by (��,��)−������(��)and is the least ℎfor which G admits (��,��)–edge irregular h-labeling. In this article, (��,��)−������(��)for some common graph families are examined. In addition, an open problem (3,2)–������(��_(��,��)),��,��>2is solved affirmatively.

Keywords

(a, d) – Irregular labeling, Edge irregular labeling, Irregular labeling, Irregularity strength, Total edge irregular labeling

Article Type

Supplemental Issue

How to Cite this Article

K., Muthugurupackiam; P., Pandiaraj; R., Gurusamy; and I., Muthuselvam (2023) "Further Results on (a, d) -total Edge Irregularity Strength of Graphs," Baghdad Science Journal: Vol. 20: Iss. 6, Article 30.
DOI: https://doi.org/10.21123/bsj.2023.8545