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Computing locating-total domination number in some rotationally symmetric graphs
Hassan Raza1, Naveed Iqbal2, Hamda Khan3
1Business School, 47863University of Shanghai for Science and Technology, Shanghai, China.
Science Progress
|November 17, 2021
Summary
This study introduces the locating-total domination number for graphs. Researchers determined this number for cycle-related graphs and convex polytopes.
Area of Science:
- Graph Theory
- Discrete Mathematics
- Combinatorics
Background:
- A locating-total dominating set is a specific type of vertex set in a graph.
- This set ensures all vertices are dominated and distinct pairs are identifiable by their neighbors.
- The minimum size of such a set is the locating-total domination number.
Purpose of the Study:
- To determine the locating-total domination number for specific graph classes.
- To extend the understanding of graph domination parameters.
- To analyze the locating-total domination number in cycle-related graphs and convex polytopes.
Main Methods:
- Graph theory definitions and properties.
- Combinatorial analysis of vertex sets.
- Case-by-case examination of graph structures.
Main Results:
- The locating-total domination number was calculated for several cycle-related graphs.
- The locating-total domination number was determined for various convex polytope graphs.
- Specific values and bounds were established for these graph classes.
Conclusions:
- The study provides exact values for the locating-total domination number in the considered graphs.
- This research contributes to the field of graph domination theory.
- The findings offer insights into the structural properties related to locating-total dominating sets.
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