- 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
- Reviewed
- Hits: 776
- Visitors: 776
- Downloads: 0
Thumbnail | File | Description | Size | Format |
---|