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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Main Authors: Ahmad Bilal, Muhammad Mobeen Munir
Format: Article
Language:English
Published: Alexandru Ioan Cuza University of Iasi 2025-08-01
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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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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issn 1843-8121
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language English
publishDate 2025-08-01
publisher Alexandru Ioan Cuza University of Iasi
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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/
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