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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Bibliographic Details
Published in:Complexity (New York, N.Y.) N.Y.), 2021, Vol.2021 (1)
Main Authors: Cheng, Rui, Ali, Gohar, Rahmat, Gul, Khan, Muhammad Yasin, Semanicova-Fenovcikova, Andrea, Liu, Jia-Bao
Format: Article
Language:English
Subjects:
Apexes
Connectivity
Graph theory
Graphs
Trees
Upper bounds
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Summary: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.
ISSN:1076-2787
1099-0526
DOI:10.1155/2021/6623277