Total Edge Irregularity Strength of The Cartesian Product of Bipartite Graphs and Paths

Title: Total Edge Irregularity Strength of The Cartesian Product of Bipartite Graphs and Paths
Creator: Wijaya, Rachel Wulan Nirmalasari; Ryan, Joe; Kalinowski, Thomas
Relation: Journal of the Indonesian Mathematical Society Vol. 29, Issue 2, p. 156-165
Publisher Link: http://dx.doi.org/10.22342/jims.29.2.1321.156-165
Publisher: Himpunan Matematika Indonesia,Indonesian Mathematical Society
Resource Type: journal article
Date: 2023
Description: 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 irregular total 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.
Subject: total edge irregularity strength; Cartesian product; bipartite graph; path
Identifier: http://hdl.handle.net/1959.13/1490492
Identifier: uon:52926
Identifier: ISSN:2086-8952
Language: eng
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