Generalized Arithmetic Staircase Graphs and Their Total Edge Irregularity Strengths
Let (Formula presented.) be a simple undirected graph with finite vertex set (Formula presented.) and edge set (Formula presented.). A total (Formula presented.) -labeling (Formula presented.) is called a total edge irregular labeling on (Formula presented.) if for any two different edges (Formula p...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI
2022
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| Subjects: | |
| Online Access: | https://repository.ugm.ac.id/278744/1/Generalized-Arithmetic-Staircase-Graphs-and-Their-Total-Edge-Irregularity-StrengthsSymmetry.pdf |
| _version_ | 1797037350595854336 |
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| author | Susanti, Yeni Wahyuni, Sri Sutjijana, Aluysius Sutopo, Sutopo Ernanto, Iwan |
| author_facet | Susanti, Yeni Wahyuni, Sri Sutjijana, Aluysius Sutopo, Sutopo Ernanto, Iwan |
| author_sort | Susanti, Yeni |
| collection | UGM |
| description | Let (Formula presented.) be a simple undirected graph with finite vertex set (Formula presented.) and edge set (Formula presented.). A total (Formula presented.) -labeling (Formula presented.) is called a total edge irregular labeling on (Formula presented.) if for any two different edges (Formula presented.) and (Formula presented.) in (Formula presented.) the numbers (Formula presented.) and (Formula presented.) are distinct. The smallest positive integer n such that (Formula presented.) can be labeled by a total edge irregular labeling is called the total edge irregularity strength of the graph (Formula presented.). In this paper, we provide the total edge irregularity strength of some asymmetric graphs and some symmetric graphs, namely generalized arithmetic staircase graphs and generalized double-staircase graphs, as the generalized forms of some existing staircase graphs. Moreover, we give the construction of the corresponding total edge irregular labelings. |
| first_indexed | 2024-03-14T00:02:00Z |
| format | Article |
| id | oai:generic.eprints.org:278744 |
| institution | Universiti Gadjah Mada |
| language | English |
| last_indexed | 2024-03-14T00:02:00Z |
| publishDate | 2022 |
| publisher | MDPI |
| record_format | dspace |
| spelling | oai:generic.eprints.org:2787442023-10-10T02:47:50Z https://repository.ugm.ac.id/278744/ Generalized Arithmetic Staircase Graphs and Their Total Edge Irregularity Strengths Susanti, Yeni Wahyuni, Sri Sutjijana, Aluysius Sutopo, Sutopo Ernanto, Iwan Mathematics and Applied Sciences Let (Formula presented.) be a simple undirected graph with finite vertex set (Formula presented.) and edge set (Formula presented.). A total (Formula presented.) -labeling (Formula presented.) is called a total edge irregular labeling on (Formula presented.) if for any two different edges (Formula presented.) and (Formula presented.) in (Formula presented.) the numbers (Formula presented.) and (Formula presented.) are distinct. The smallest positive integer n such that (Formula presented.) can be labeled by a total edge irregular labeling is called the total edge irregularity strength of the graph (Formula presented.). In this paper, we provide the total edge irregularity strength of some asymmetric graphs and some symmetric graphs, namely generalized arithmetic staircase graphs and generalized double-staircase graphs, as the generalized forms of some existing staircase graphs. Moreover, we give the construction of the corresponding total edge irregular labelings. MDPI 2022-09-06 Article PeerReviewed application/pdf en https://repository.ugm.ac.id/278744/1/Generalized-Arithmetic-Staircase-Graphs-and-Their-Total-Edge-Irregularity-StrengthsSymmetry.pdf Susanti, Yeni and Wahyuni, Sri and Sutjijana, Aluysius and Sutopo, Sutopo and Ernanto, Iwan (2022) Generalized Arithmetic Staircase Graphs and Their Total Edge Irregularity Strengths. symmetry, 14 (9). pp. 1-18. ISSN 20738994 https://www.mdpi.com/2073-8994/14/9/1853 https://doi.org/10.3390/sym14091853 |
| spellingShingle | Mathematics and Applied Sciences Susanti, Yeni Wahyuni, Sri Sutjijana, Aluysius Sutopo, Sutopo Ernanto, Iwan Generalized Arithmetic Staircase Graphs and Their Total Edge Irregularity Strengths |
| title | Generalized Arithmetic Staircase Graphs and Their Total Edge Irregularity Strengths |
| title_full | Generalized Arithmetic Staircase Graphs and Their Total Edge Irregularity Strengths |
| title_fullStr | Generalized Arithmetic Staircase Graphs and Their Total Edge Irregularity Strengths |
| title_full_unstemmed | Generalized Arithmetic Staircase Graphs and Their Total Edge Irregularity Strengths |
| title_short | Generalized Arithmetic Staircase Graphs and Their Total Edge Irregularity Strengths |
| title_sort | generalized arithmetic staircase graphs and their total edge irregularity strengths |
| topic | Mathematics and Applied Sciences |
| url | https://repository.ugm.ac.id/278744/1/Generalized-Arithmetic-Staircase-Graphs-and-Their-Total-Edge-Irregularity-StrengthsSymmetry.pdf |
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