Abstract: A dominating set of a connected graph G = (V, E) is a subset D of V (G) such that every vertex of G is either in D or adjacent to a vertex in D. A resolving set of a connected graph G is a subset D of V (G) such that each vertex v of G has a unique representation with respect to D. A dominant resolving set of a graph G is a subset D of V (G) that resolves all vertices of G and dominates G. The dominant metric dimension, Ddim(G), is the cardinality of the smallest such set. The dominant metric dimension of a graph combines metric dimension (location identification) with domination (coverage), making it ideal for sensor networks that require both unique positioning and full coverage. Similarly, a dominant edge resolving set of a connected graph G is a vertex subset D of V that resolves all edges and is a covering of G. Star fan graphs are composite graph structures formed by attaching fan graphs to the pendant vertices of a star graph, creating hierarchical networks that are useful for modeling hub-and-spoke systems with additional path structures. This paper computes the dominant metric dimension and dominant edge metric dimension of star fan graphs.
| Published in | Applied and Computational Mathematics (Volume 15, Issue 3) |
| DOI | 10.11648/j.acm.20261503.13 |
| Page(s) | 89-94 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
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Copyright © The Author(s), 2026. Published by Science Publishing Group |
Dominant Metric Dimension, Dominant Edge Metric Dimension, Star Fan Graph
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APA Style
Mathew, S. V., Vijayalakshmi, V. (2026). Dominant Metric Dimension of Star Fan Graphs. Applied and Computational Mathematics, 15(3), 89-94. https://doi.org/10.11648/j.acm.20261503.13
ACS Style
Mathew, S. V.; Vijayalakshmi, V. Dominant Metric Dimension of Star Fan Graphs. Appl. Comput. Math. 2026, 15(3), 89-94. doi: 10.11648/j.acm.20261503.13
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Download@article{10.11648/j.acm.20261503.13,
author = {Sali Vadakkethil Mathew and Venkatajalam Vijayalakshmi},
title = {Dominant Metric Dimension of Star Fan Graphs
},
journal = {Applied and Computational Mathematics},
volume = {15},
number = {3},
pages = {89-94},
doi = {10.11648/j.acm.20261503.13},
url = {https://doi.org/10.11648/j.acm.20261503.13},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20261503.13},
abstract = {Abstract: A dominating set of a connected graph G = (V, E) is a subset D of V (G) such that every vertex of G is either in D or adjacent to a vertex in D. A resolving set of a connected graph G is a subset D of V (G) such that each vertex v of G has a unique representation with respect to D. A dominant resolving set of a graph G is a subset D of V (G) that resolves all vertices of G and dominates G. The dominant metric dimension, Ddim(G), is the cardinality of the smallest such set. The dominant metric dimension of a graph combines metric dimension (location identification) with domination (coverage), making it ideal for sensor networks that require both unique positioning and full coverage. Similarly, a dominant edge resolving set of a connected graph G is a vertex subset D of V that resolves all edges and is a covering of G. Star fan graphs are composite graph structures formed by attaching fan graphs to the pendant vertices of a star graph, creating hierarchical networks that are useful for modeling hub-and-spoke systems with additional path structures. This paper computes the dominant metric dimension and dominant edge metric dimension of star fan graphs.
},
year = {2026}
}
TY - JOUR T1 - Dominant Metric Dimension of Star Fan Graphs AU - Sali Vadakkethil Mathew AU - Venkatajalam Vijayalakshmi Y1 - 2026/06/10 PY - 2026 N1 - https://doi.org/10.11648/j.acm.20261503.13 DO - 10.11648/j.acm.20261503.13 T2 - Applied and Computational Mathematics JF - Applied and Computational Mathematics JO - Applied and Computational Mathematics SP - 89 EP - 94 PB - Science Publishing Group SN - 2328-5613 UR - https://doi.org/10.11648/j.acm.20261503.13 AB - Abstract: A dominating set of a connected graph G = (V, E) is a subset D of V (G) such that every vertex of G is either in D or adjacent to a vertex in D. A resolving set of a connected graph G is a subset D of V (G) such that each vertex v of G has a unique representation with respect to D. A dominant resolving set of a graph G is a subset D of V (G) that resolves all vertices of G and dominates G. The dominant metric dimension, Ddim(G), is the cardinality of the smallest such set. The dominant metric dimension of a graph combines metric dimension (location identification) with domination (coverage), making it ideal for sensor networks that require both unique positioning and full coverage. Similarly, a dominant edge resolving set of a connected graph G is a vertex subset D of V that resolves all edges and is a covering of G. Star fan graphs are composite graph structures formed by attaching fan graphs to the pendant vertices of a star graph, creating hierarchical networks that are useful for modeling hub-and-spoke systems with additional path structures. This paper computes the dominant metric dimension and dominant edge metric dimension of star fan graphs. VL - 15 IS - 3 ER -
Department of Mathematics, Anna University, Chennai, India
Department of Mathematics, Anna University, Chennai, India
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