Abstract

LENES, Eber; GARCIA, Henry; FIGUEROA, Ariel  and  MERCADO B., Fabian. Extremal graphs for α-index. Integración - UIS [online]. 2020, vol.38, n.1, pp.15-31.  Epub Feb 27, 2020. ISSN 0120-419X.  https://doi.org/10.18273/revint.v38n1-2020002.

Let N(G) be the number of vertices of the graph G. Let Pl(Bi) be the tree obtained of the path Pl and the trees B1,B2,...,Bl by identifying the root vertex of Bi with the i-th vertex of Pl. Let V m n = {Pl(Bi) : N(Pl(Bi)) = n;N(Bi) ≥ 2;l ≥ m}. In this paper, we determine the tree that has the largest α-index among all the trees in V m n .

MSC2010: 05C50, 05C76, 15A18, 05C12, 05C75.

Keywords : Caterpillar; diameter; distance; index; tree..

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