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Joe Ryan
The University of Newcastle, NSW, Australia
Mathematics

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Total Edge Irregularity Strength of the Cartesian Product of Bipartite Graphs and Paths Rachel Wulan Nirmalasari Wijaya; Joe Ryan; Thomas Kalinowski
Journal of the Indonesian Mathematical Society VOLUME 29 NUMBER 2 (JULY 2023)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.29.2.1321.156-165

Abstract

For a simple graph G = (V (G), E(G)), a total labeling ∂ is called an edge irregular total k-labeling of G if ∂ : V (G) ∪ E(G) → {1, 2, . . . , k} such that for any two different edges uv and u'v' in E(G), we have wt∂(uv) not equal to wt∂(u'v') where wt∂(uv) = ∂(u) + ∂(v) + ∂(uv). The minimum k for which G has an edge irregulartotal k-labeling is called the total edge irregularity strength, denoted by tes(G). It is known that ceil((|E(G)|+2)/3) is a lower bound for the total edge irregularity strength of a graph G. In this paper we prove that if G is a bipartite graph for which this bound is tight then this is also true for Cartesian product of G with any path.
Co-Authors Rachel Wulan Nirmalasari Wijaya Thomas Kalinowski