On the general sum-connectivity index of connected graphs with given order and girth
| Main Author: | Tomescu, Ioan; Faculty of Mathematics and Computer Science, University of Bucharest, Str. Academiei, 14, Bucharest, Romania |
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| Format: | Article info application/pdf eJournal |
| Bahasa: | eng |
| Terbitan: |
GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB
, 2016
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| Subjects: | |
| Online Access: |
http://www.ejgta.org/index.php/ejgta/article/view/173 http://www.ejgta.org/index.php/ejgta/article/view/173/pdf_1 |
Daftar Isi:
- In this paper, we show that in the classof connected graphs $G$ of order $n\geq 3$ having girth at least equal to $k$, $3\leq k\leq n$, the unique graph $G$ having minimum general sum-connectivity index $\chi _{\alpha }(G)$ consists of $C_{k}$ and $n-k$ pendant vertices adjacent to a unique vertex of $C_{k}$, if $-1\leq \alpha <0$. This property does not hold for zeroth-order general Randi\' c index $^{0}R_{\alpha}(G)$.