On the Exact Values of HZ-Index for the Graphs under Operations

Topological index (TI) is a function from the set of graphs to the set of real numbers that associates a unique real number to each graph, and two graphs necessarily have the same value of the TI if these are structurally isomorphic. In this note, we compute the HZ−index of the four generalized sum...

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Autores principales:	Dalal Awadh Alrowaili, Saira Javed, Muhammad Javaid
Formato:	article
Lenguaje:	EN
Publicado:	Hindawi Limited 2021
Materias:	Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/b20a1f86161840b782a2b17a574a2c83
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spelling	oai:doaj.org-article:b20a1f86161840b782a2b17a574a2c832021-11-29T00:56:59ZOn the Exact Values of HZ-Index for the Graphs under Operations2314-478510.1155/2021/3304939https://doaj.org/article/b20a1f86161840b782a2b17a574a2c832021-01-01T00:00:00Zhttp://dx.doi.org/10.1155/2021/3304939https://doaj.org/toc/2314-4785Topological index (TI) is a function from the set of graphs to the set of real numbers that associates a unique real number to each graph, and two graphs necessarily have the same value of the TI if these are structurally isomorphic. In this note, we compute the HZ−index of the four generalized sum graphs in the form of the various Zagreb indices of their factor graphs. These graphs are obtained by the strong product of the graphs G and DkG, where Dk∈Sk,Rk,Qk,Tk represents the four generalized subdivision-related operations for the integral value of k≥1 and DkG is a graph that is obtained by applying Dk on G. At the end, as an illustration, we compute the HZ−index of the generalized sum graphs for exactly k=1 and compare the obtained results.Dalal Awadh AlrowailiSaira JavedMuhammad JavaidHindawi LimitedarticleMathematicsQA1-939ENJournal of Mathematics, Vol 2021 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Mathematics QA1-939
spellingShingle	Mathematics QA1-939 Dalal Awadh Alrowaili Saira Javed Muhammad Javaid On the Exact Values of HZ-Index for the Graphs under Operations
description	Topological index (TI) is a function from the set of graphs to the set of real numbers that associates a unique real number to each graph, and two graphs necessarily have the same value of the TI if these are structurally isomorphic. In this note, we compute the HZ−index of the four generalized sum graphs in the form of the various Zagreb indices of their factor graphs. These graphs are obtained by the strong product of the graphs G and DkG, where Dk∈Sk,Rk,Qk,Tk represents the four generalized subdivision-related operations for the integral value of k≥1 and DkG is a graph that is obtained by applying Dk on G. At the end, as an illustration, we compute the HZ−index of the generalized sum graphs for exactly k=1 and compare the obtained results.
format	article
author	Dalal Awadh Alrowaili Saira Javed Muhammad Javaid
author_facet	Dalal Awadh Alrowaili Saira Javed Muhammad Javaid
author_sort	Dalal Awadh Alrowaili
title	On the Exact Values of HZ-Index for the Graphs under Operations
title_short	On the Exact Values of HZ-Index for the Graphs under Operations
title_full	On the Exact Values of HZ-Index for the Graphs under Operations
title_fullStr	On the Exact Values of HZ-Index for the Graphs under Operations
title_full_unstemmed	On the Exact Values of HZ-Index for the Graphs under Operations
title_sort	on the exact values of hz-index for the graphs under operations
publisher	Hindawi Limited
publishDate	2021
url	https://doaj.org/article/b20a1f86161840b782a2b17a574a2c83
work_keys_str_mv	AT dalalawadhalrowaili ontheexactvaluesofhzindexforthegraphsunderoperations AT sairajaved ontheexactvaluesofhzindexforthegraphsunderoperations AT muhammadjavaid ontheexactvaluesofhzindexforthegraphsunderoperations
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On the Exact Values of HZ-Index for the Graphs under Operations

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