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 |
| Published: |
Wiley
2021-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2021/6623277 |
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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. |
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| ISSN: | 1076-2787 1099-0526 |