Investigation of General Power Sum-Connectivity Index for Some Classes of Extremal Graphs

In this work, we introduce a new topological index called a general power sum-connectivity index and we discuss this graph invariant for some classes of extremal graphs. This index is defined by YαG=∑uv∈EGdudu+dvdvα, where du and dv represent the degree of vertices u and v, respectively, and α≥1. A...

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Main Authors: Rui Cheng, Gohar Ali, Gul Rahmat, Muhammad Yasin Khan, Andrea Semanicova-Fenovcikova, Jia-Bao Liu
Format: Article
Language:English
Published: Wiley 2021-01-01
Series:Complexity
Online Access:http://dx.doi.org/10.1155/2021/6623277
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author Rui Cheng
Gohar Ali
Gul Rahmat
Muhammad Yasin Khan
Andrea Semanicova-Fenovcikova
Jia-Bao Liu
author_facet Rui Cheng
Gohar Ali
Gul Rahmat
Muhammad Yasin Khan
Andrea Semanicova-Fenovcikova
Jia-Bao Liu
author_sort Rui Cheng
collection DOAJ
description In this work, we introduce a new topological index called a general power sum-connectivity index and we discuss this graph invariant for some classes of extremal graphs. This index is defined by YαG=∑uv∈EGdudu+dvdvα, where du and dv represent the degree of vertices u and v, respectively, and α≥1. A connected graph G is called a k-generalized quasi-tree if there exists a subset Vk⊂VG of cardinality k such that the graph G−Vk is a tree but for any subset Vk−1⊂VG of cardinality k−1, the graph G−Vk−1 is not a tree. In this work, we find a sharp lower and some sharp upper bounds for this new sum-connectivity index.
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institution OA Journals
issn 1076-2787
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publishDate 2021-01-01
publisher Wiley
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series Complexity
spelling doaj-art-7e2e8da163bb4b85b55300a5e97034972025-08-20T02:08:26ZengWileyComplexity1076-27871099-05262021-01-01202110.1155/2021/66232776623277Investigation of General Power Sum-Connectivity Index for Some Classes of Extremal GraphsRui Cheng0Gohar Ali1Gul Rahmat2Muhammad Yasin Khan3Andrea Semanicova-Fenovcikova4Jia-Bao Liu5School of Resources and Environment, Anhui Agricultural University, Hefei 230036, ChinaDepartment of Mathematics, Islamia College, Peshawar, Khyber Pakhtunkhwa, PakistanDepartment of Mathematics, Islamia College, Peshawar, Khyber Pakhtunkhwa, PakistanDepartment of Mathematics, Islamia College, Peshawar, Khyber Pakhtunkhwa, PakistanDepartment of Applied Mathematics and Informatics, Faculty of Mechanical Engineering, Technical University in Kosice, Letna 9, Kosice, SlovakiaSchool of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, ChinaIn this work, we introduce a new topological index called a general power sum-connectivity index and we discuss this graph invariant for some classes of extremal graphs. This index is defined by YαG=∑uv∈EGdudu+dvdvα, where du and dv represent the degree of vertices u and v, respectively, and α≥1. A connected graph G is called a k-generalized quasi-tree if there exists a subset Vk⊂VG of cardinality k such that the graph G−Vk is a tree but for any subset Vk−1⊂VG of cardinality k−1, the graph G−Vk−1 is not a tree. In this work, we find a sharp lower and some sharp upper bounds for this new sum-connectivity index.http://dx.doi.org/10.1155/2021/6623277
spellingShingle Rui Cheng
Gohar Ali
Gul Rahmat
Muhammad Yasin Khan
Andrea Semanicova-Fenovcikova
Jia-Bao Liu
Investigation of General Power Sum-Connectivity Index for Some Classes of Extremal Graphs
Complexity
title Investigation of General Power Sum-Connectivity Index for Some Classes of Extremal Graphs
title_full Investigation of General Power Sum-Connectivity Index for Some Classes of Extremal Graphs
title_fullStr Investigation of General Power Sum-Connectivity Index for Some Classes of Extremal Graphs
title_full_unstemmed Investigation of General Power Sum-Connectivity Index for Some Classes of Extremal Graphs
title_short Investigation of General Power Sum-Connectivity Index for Some Classes of Extremal Graphs
title_sort investigation of general power sum connectivity index for some classes of extremal graphs
url http://dx.doi.org/10.1155/2021/6623277
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