Explicit Formulas for the Complexity of Networks Produced by New Duplicating Corona and Cartesian Product
One important algebraic invariant in networks is complexity. This invariant ensures the accuracy and dependability of the network. In this paper, we employ a combinatorial approach to determine the graph’s complexity. A fundamental set of building blocks (basic graphs) will serve as the foundation f...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2024-01-01
|
| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2024/9131329 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850228453518868480 |
|---|---|
| author | Mohamed R. Zeen El Deen Walaa A. Aboamer Hamed M. El-Sherbiny |
| author_facet | Mohamed R. Zeen El Deen Walaa A. Aboamer Hamed M. El-Sherbiny |
| author_sort | Mohamed R. Zeen El Deen |
| collection | DOAJ |
| description | One important algebraic invariant in networks is complexity. This invariant ensures the accuracy and dependability of the network. In this paper, we employ a combinatorial approach to determine the graph’s complexity. A fundamental set of building blocks (basic graphs) will serve as the foundation for all the graphs we investigate, after which we will analyze the individual blocks and the ways in which they are connected. We compute the spectrum and complexity of a number of fundamental graphs and then we employ the novel duplication corona and Cartesian product operations to construct advanced networks from these graphs. Specifically, straightforward formulas are derived for the complexity of the networks created by the new duplicating corona of the regular graphs (prism, diagonal prism, cycle, complete graph, shadow of the cycle, and Petersen graph) with some families of graphs. Furthermore, using Cartesian product operation, evident and specific formulas for the complexity of the prism of the grid graph Gl,κ, the prism of the stacked book graph Bl,s, the diagonal plane prism grid graph, and the prism of the cylindrical graph Cl,κ are derived. |
| format | Article |
| id | doaj-art-2b9f82f490c94901b0019e29fcf0680d |
| institution | OA Journals |
| issn | 2314-4785 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-2b9f82f490c94901b0019e29fcf0680d2025-08-20T02:04:31ZengWileyJournal of Mathematics2314-47852024-01-01202410.1155/2024/9131329Explicit Formulas for the Complexity of Networks Produced by New Duplicating Corona and Cartesian ProductMohamed R. Zeen El Deen0Walaa A. Aboamer1Hamed M. El-Sherbiny2Department of Mathematics and Computer ScienceDepartment of Mathematics and Computer ScienceDepartment of Mathematics and Computer ScienceOne important algebraic invariant in networks is complexity. This invariant ensures the accuracy and dependability of the network. In this paper, we employ a combinatorial approach to determine the graph’s complexity. A fundamental set of building blocks (basic graphs) will serve as the foundation for all the graphs we investigate, after which we will analyze the individual blocks and the ways in which they are connected. We compute the spectrum and complexity of a number of fundamental graphs and then we employ the novel duplication corona and Cartesian product operations to construct advanced networks from these graphs. Specifically, straightforward formulas are derived for the complexity of the networks created by the new duplicating corona of the regular graphs (prism, diagonal prism, cycle, complete graph, shadow of the cycle, and Petersen graph) with some families of graphs. Furthermore, using Cartesian product operation, evident and specific formulas for the complexity of the prism of the grid graph Gl,κ, the prism of the stacked book graph Bl,s, the diagonal plane prism grid graph, and the prism of the cylindrical graph Cl,κ are derived.http://dx.doi.org/10.1155/2024/9131329 |
| spellingShingle | Mohamed R. Zeen El Deen Walaa A. Aboamer Hamed M. El-Sherbiny Explicit Formulas for the Complexity of Networks Produced by New Duplicating Corona and Cartesian Product Journal of Mathematics |
| title | Explicit Formulas for the Complexity of Networks Produced by New Duplicating Corona and Cartesian Product |
| title_full | Explicit Formulas for the Complexity of Networks Produced by New Duplicating Corona and Cartesian Product |
| title_fullStr | Explicit Formulas for the Complexity of Networks Produced by New Duplicating Corona and Cartesian Product |
| title_full_unstemmed | Explicit Formulas for the Complexity of Networks Produced by New Duplicating Corona and Cartesian Product |
| title_short | Explicit Formulas for the Complexity of Networks Produced by New Duplicating Corona and Cartesian Product |
| title_sort | explicit formulas for the complexity of networks produced by new duplicating corona and cartesian product |
| url | http://dx.doi.org/10.1155/2024/9131329 |
| work_keys_str_mv | AT mohamedrzeeneldeen explicitformulasforthecomplexityofnetworksproducedbynewduplicatingcoronaandcartesianproduct AT walaaaaboamer explicitformulasforthecomplexityofnetworksproducedbynewduplicatingcoronaandcartesianproduct AT hamedmelsherbiny explicitformulasforthecomplexityofnetworksproducedbynewduplicatingcoronaandcartesianproduct |