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A constructive method to determine the total vertex irregularity strength of two flower graph variants
Nurdin Hinding1, Nurtiti Sunusi2, Sarti Mutmainnah3
1Graph Theory Research Group, Department of Mathematics, Faculty of Mathematics and Nature Sciences, Hasanuddin University, Jl. Perintis Kemerdekaan Km. 10, Makassar City, 90245, Indonesia.
Methodsx
|September 24, 2025
Summary
This study introduces a new method for total vertex irregular labeling in specific flower graphs. It determines the exact total vertex irregularity strength for modified sunflower and flower petal graphs, offering a replicable strategy for similar graph structures.
Area of Science:
- Discrete Mathematics
- Graph Theory
- Combinatorics
Background:
- Graph labeling is a key area in discrete mathematics.
- Total vertex irregular labeling requires distinct vertex weights after assigning labels to vertices and edges.
- Investigating irregular labeling for specific graph classes like flower graphs is an active research area.
Purpose of the Study:
- To develop a constructive method for determining the total vertex irregularity strength of two flower graph variants.
- To analyze the total vertex irregularity strength of modified sunflower graphs and flower petal graphs.
- To establish a replicable labeling strategy for graphs with similar structural properties.
Main Methods:
- Proposed a constructive approach for assigning labels to vertices and edges.
- Employed explicit label assignments and verified the distinctness of resulting vertex weights.
- Analyzed two specific flower graph variants with two distinct vertex degrees.
Main Results:
- Determined the total vertex irregularity strength of the modified sunflower graph to be n/2 + 1.
- Calculated the total vertex irregularity strength of the flower petal graph as ceil((n^2 - 2n + 2)/3).
- Highlighted that the differing strengths are due to the distinct structural properties of the two graphs.
Conclusions:
- The study successfully determined the exact total vertex irregularity strength for the investigated flower graph variants.
- The proposed constructive method provides a systematic approach for irregular graph labeling.
- Findings contribute to the understanding of irregular graph labeling and have potential applications in network analysis.
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