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: | , , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| 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. |
| format | Article |
| id | doaj-art-7e2e8da163bb4b85b55300a5e9703497 |
| institution | OA Journals |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| 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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