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Ioan Tomescu
Faculty of Mathematics and Computer Science, University of Bucharest, Str. Academiei, 14, Bucharest, Romania
Electrical & Electronics Engineering

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On the general sum-connectivity index of connected graphs with given order and girth Ioan Tomescu
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 4, No 1 (2016): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2016.4.1.1

Abstract

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 $^{0}R_{\alpha}(G)$.
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