UPPER BOUNDS FOR THE PRODUCT HARARY–FURTULA INDEX OF SPLICE AND THORN GRAPHS
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Department of Mathematics Government Arts College ,Mutlur 608 002 India
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Abstract
This paper studies upper bounds for the product Harary–Furtula index RD∗ (G) of splice and thorn graphs. For the splice graph obtained by joining selected vertices of two connected graphs with a new edge, the changes in vertex degrees and distances are analyzed to derive an upper bound in terms of the structural parameters of the constituent graphs. The study is further extended to thorn graphs formed by attaching pendant vertices to the vertices of a given graph. Suitable parameters involving the number of pendant vertices, degree bounds, and distance contributions are introduced to establish an upper bound for the product Harary–Furtula index. A special case in which the same number of pendant vertices is attached to every vertex is also considered. The results provide useful inequalities for the product Harary–Furtula index under these graph constructions.
Keywords
Product Harary–Furtula Index Splice Graph Thorn Graph Graph Operations Upper Bounds.
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Double-Blind Peer Review
License:
CC BY-NC 4.0
Volume/Issue:
Volume 02, Issue 8
Review Rounds:
2
Article Type:
Research Article
Publication Date:
Aug 21 2026
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Kandan, P. & Niranjan, S. (2026). Upper Bounds for the Product Harary–Furtula Index of Splice and Thorn Graphs. International Journal of Science, Strategic Management and Technology, 02(8), 1-9. https://doi.org/10.55041/ijsmt.v2i8.058
Kandan, P., and S. Niranjan. "Upper Bounds for the Product Harary–Furtula Index of Splice and Thorn Graphs." International Journal of Science, Strategic Management and Technology, vol. 02, no. 8, 2026, pp. 1-9. doi:https://doi.org/10.55041/ijsmt.v2i8.058.
Kandan, P., and S. Niranjan. "Upper Bounds for the Product Harary–Furtula Index of Splice and Thorn Graphs." International Journal of Science, Strategic Management and Technology 02, no. 8 (2026): 1-9. https://doi.org/https://doi.org/10.55041/ijsmt.v2i8.058.
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