First Hyper Zagreb Spectral Radii of Splitting and Shadow Graphs
The spectral radius RS of graph G is a spectral invariant derived from the eigenvalues of the associated matrix for a graph G. It is widely used in fields such as computer science, chemistry, biology, and network analysis. A notable expansion of this notion is the First Hyper Zagreb spectral radius,...
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Alexandru Ioan Cuza University of Iasi
2025-08-01
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| Series: | Scientific Annals of Computer Science |
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| Online Access: | https://publications.info.uaic.ro/scientific-annals-of-computer-science/sacs-volumes/xxxv-2/first-hyper-zagreb-spectral-radii-of-splitting-and-shadow-graphs/ |
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| _version_ | 1849240659805863936 |
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| author | Ahmad Bilal Muhammad Mobeen Munir |
| author_facet | Ahmad Bilal Muhammad Mobeen Munir |
| author_sort | Ahmad Bilal |
| collection | DOAJ |
| description | The spectral radius RS of graph G is a spectral invariant derived from the eigenvalues of the associated matrix for a graph G. It is widely used in fields such as computer science, chemistry, biology, and network analysis. A notable expansion of this notion is the First Hyper Zagreb spectral radius, RSHZ1(G), which is defined as the largest absolute eigenvalues of the First Hyper Zagreb matrix. This study examines the behaviour of First Hyper Zagreb spectral radius under two graph operations, generalized shadow and generalized splitting. We compare RSHZ1(Splq(G)) and RSHZ1(Shq(G)) with the RSHZ1(G) of base graph G. Our study explores the impact of graph operations on spectral features, providing structural insights and analytical connections. The findings enhance our understanding of spectral graph theory and have potential implications in molecular computing and complicated network research, where graph operations are commonly used.
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| format | Article |
| id | doaj-art-b5dc82270eaf4d4d826d5a238ee6f91f |
| institution | Kabale University |
| issn | 1843-8121 2248-2695 |
| language | English |
| publishDate | 2025-08-01 |
| publisher | Alexandru Ioan Cuza University of Iasi |
| record_format | Article |
| series | Scientific Annals of Computer Science |
| spelling | doaj-art-b5dc82270eaf4d4d826d5a238ee6f91f2025-08-20T04:00:28ZengAlexandru Ioan Cuza University of IasiScientific Annals of Computer Science1843-81212248-26952025-08-01XXXV212313810.47743/SACS.2025.2.123First Hyper Zagreb Spectral Radii of Splitting and Shadow GraphsAhmad Bilal0Muhammad Mobeen Munir1University of Rasul, Mandi Bahauddin, PakistanDepartment of Mathematics, University of the Punjab, Quaid-e-Azam Campus, Lahore, PakistanThe spectral radius RS of graph G is a spectral invariant derived from the eigenvalues of the associated matrix for a graph G. It is widely used in fields such as computer science, chemistry, biology, and network analysis. A notable expansion of this notion is the First Hyper Zagreb spectral radius, RSHZ1(G), which is defined as the largest absolute eigenvalues of the First Hyper Zagreb matrix. This study examines the behaviour of First Hyper Zagreb spectral radius under two graph operations, generalized shadow and generalized splitting. We compare RSHZ1(Splq(G)) and RSHZ1(Shq(G)) with the RSHZ1(G) of base graph G. Our study explores the impact of graph operations on spectral features, providing structural insights and analytical connections. The findings enhance our understanding of spectral graph theory and have potential implications in molecular computing and complicated network research, where graph operations are commonly used. https://publications.info.uaic.ro/scientific-annals-of-computer-science/sacs-volumes/xxxv-2/first-hyper-zagreb-spectral-radii-of-splitting-and-shadow-graphs/first hyper zagreb matrixshadow graphsplitting graphfirst hyper zagreb eigenvaluesfirst hyper zagreb spectral radius |
| spellingShingle | Ahmad Bilal Muhammad Mobeen Munir First Hyper Zagreb Spectral Radii of Splitting and Shadow Graphs Scientific Annals of Computer Science first hyper zagreb matrix shadow graph splitting graph first hyper zagreb eigenvalues first hyper zagreb spectral radius |
| title | First Hyper Zagreb Spectral Radii of Splitting and Shadow Graphs |
| title_full | First Hyper Zagreb Spectral Radii of Splitting and Shadow Graphs |
| title_fullStr | First Hyper Zagreb Spectral Radii of Splitting and Shadow Graphs |
| title_full_unstemmed | First Hyper Zagreb Spectral Radii of Splitting and Shadow Graphs |
| title_short | First Hyper Zagreb Spectral Radii of Splitting and Shadow Graphs |
| title_sort | first hyper zagreb spectral radii of splitting and shadow graphs |
| topic | first hyper zagreb matrix shadow graph splitting graph first hyper zagreb eigenvalues first hyper zagreb spectral radius |
| url | https://publications.info.uaic.ro/scientific-annals-of-computer-science/sacs-volumes/xxxv-2/first-hyper-zagreb-spectral-radii-of-splitting-and-shadow-graphs/ |
| work_keys_str_mv | AT ahmadbilal firsthyperzagrebspectralradiiofsplittingandshadowgraphs AT muhammadmobeenmunir firsthyperzagrebspectralradiiofsplittingandshadowgraphs |