On the Reformulated Multiplicative First Zagreb Index of Trees and Unicyclic Graphs

The multiplicative first Zagreb index of a graph H is defined as the product of the squares of the degrees of vertices of H. The line graph of a graph H is denoted by LH and is defined as the graph whose vertex set is the edge set of H where two vertices of LH are adjacent if and only if they are ad...

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Autores principales:	Akbar Ali, Atif Nadeem, Zahid Raza, Wael W. Mohammed, Elsayed M. Elsayed
Formato:	article
Lenguaje:	EN
Publicado:	Hindawi Limited 2021
Materias:	Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/ffe15adde03149c3aae653d95fb173c3
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spelling	oai:doaj.org-article:ffe15adde03149c3aae653d95fb173c32021-11-08T02:37:15ZOn the Reformulated Multiplicative First Zagreb Index of Trees and Unicyclic Graphs1607-887X10.1155/2021/3324357https://doaj.org/article/ffe15adde03149c3aae653d95fb173c32021-01-01T00:00:00Zhttp://dx.doi.org/10.1155/2021/3324357https://doaj.org/toc/1607-887XThe multiplicative first Zagreb index of a graph H is defined as the product of the squares of the degrees of vertices of H. The line graph of a graph H is denoted by LH and is defined as the graph whose vertex set is the edge set of H where two vertices of LH are adjacent if and only if they are adjacent in H. The multiplicative first Zagreb index of the line graph of a graph H is referred to as the reformulated multiplicative first Zagreb index of H. This paper gives characterization of the unique graph attaining the minimum or maximum value of the reformulated multiplicative first Zagreb index in the class of all (i) trees of a fixed order (ii) connected unicyclic graphs of a fixed order.Akbar AliAtif NadeemZahid RazaWael W. MohammedElsayed M. ElsayedHindawi LimitedarticleMathematicsQA1-939ENDiscrete Dynamics in Nature and Society, Vol 2021 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Mathematics QA1-939
spellingShingle	Mathematics QA1-939 Akbar Ali Atif Nadeem Zahid Raza Wael W. Mohammed Elsayed M. Elsayed On the Reformulated Multiplicative First Zagreb Index of Trees and Unicyclic Graphs
description	The multiplicative first Zagreb index of a graph H is defined as the product of the squares of the degrees of vertices of H. The line graph of a graph H is denoted by LH and is defined as the graph whose vertex set is the edge set of H where two vertices of LH are adjacent if and only if they are adjacent in H. The multiplicative first Zagreb index of the line graph of a graph H is referred to as the reformulated multiplicative first Zagreb index of H. This paper gives characterization of the unique graph attaining the minimum or maximum value of the reformulated multiplicative first Zagreb index in the class of all (i) trees of a fixed order (ii) connected unicyclic graphs of a fixed order.
format	article
author	Akbar Ali Atif Nadeem Zahid Raza Wael W. Mohammed Elsayed M. Elsayed
author_facet	Akbar Ali Atif Nadeem Zahid Raza Wael W. Mohammed Elsayed M. Elsayed
author_sort	Akbar Ali
title	On the Reformulated Multiplicative First Zagreb Index of Trees and Unicyclic Graphs
title_short	On the Reformulated Multiplicative First Zagreb Index of Trees and Unicyclic Graphs
title_full	On the Reformulated Multiplicative First Zagreb Index of Trees and Unicyclic Graphs
title_fullStr	On the Reformulated Multiplicative First Zagreb Index of Trees and Unicyclic Graphs
title_full_unstemmed	On the Reformulated Multiplicative First Zagreb Index of Trees and Unicyclic Graphs
title_sort	on the reformulated multiplicative first zagreb index of trees and unicyclic graphs
publisher	Hindawi Limited
publishDate	2021
url	https://doaj.org/article/ffe15adde03149c3aae653d95fb173c3
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On the Reformulated Multiplicative First Zagreb Index of Trees and Unicyclic Graphs

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