Abstract
We show that on cactus graphs the Szeged index is bounded above by twice the Wiener index. For the revised Szeged index the situation is reversed if the graph class is further restricted. Namely, if all blocks of a cactus graph are cycles, then its revised Szeged index is bounded below by twice its Wiener index. Additionally, we show that these bounds are sharp and examine the cases of equality. Along the way, we provide a formulation of the revised Szeged index as a sum over vertices, which proves very helpful, and may be interesting in other contexts.
Original language | English |
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Article number | 05C09 |
Number of pages | 12 |
Journal | Ars Mathematica Contemporanea |
Volume | 23 |
Issue number | 3 |
DOIs | |
Publication status | Published - 11 Jan 2023 |
Keywords
- (Revised) Szeged index
- cactus graphs
- Wiener index
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Geometry and Topology
- Algebra and Number Theory