caa a22 4500 605508933 CHVBK 20210128100638.0 cr unu---uuuuu 210128e20151001xx s 000 0 eng 10.1007/s00010-014-0324-0 doi (NATIONALLICENCE)springer-10.1007/s00010-014-0324-0 Hyperbolicity in the corona and join of graphs [Elektronische Daten] [Walter Carballosa, José Rodríguez, José Sigarreta] If X is a geodesic metric space and $${x_1, x_2, x_3 \in X}$$ x 1 , x 2 , x 3 ∈ X , a geodesic triangle T={x 1, x 2, x 3} is the union of the three geodesics [x 1 x 2], [x 2 x 3] and [x 3 x 1] in X. The space X is δ-hyperbolic (in the Gromov sense) if any side of T is contained in a δ-neighborhood of the union of the two other sides, for every geodesic triangle T in X. If X is hyperbolic, we denote by δ(X) the sharp hyperbolicity constant of X, i.e. δ(X)= inf{δ≥ 0: X is δ-hyperbolic}. In this paper we characterize the hyperbolic product graphs for graph join G+ H and the corona $${G\odot\mathcal H: G + H}$$ G ⊙ H : G + H is always hyperbolic, and $${G\odot\mathcal H}$$ G ⊙ H is hyperbolic if and only if G is hyperbolic. Furthermore, we obtain simple formulae for the hyperbolicity constant of the graph join G + H and the corona $${G \odot \mathcal H}$$ G ⊙ H . Springer Basel, 2014 Graph join nationallicence Corona graph nationallicence Gromov hyperbolicity nationallicence Infinite graph nationallicence Carballosa Walter Consejo Nacional de Ciencia y Tecnología (CONACYT) and Universidad Autónoma de Zacatecas, Paseo la Bufa, int. Calzada Solidaridad, 98060, Zacatecas, ZAC, Mexico aut Rodríguez José Department of Mathematics, Universidad Carlos III de Madrid, Av. de la Universidad 30, 28911, Leganés, Madrid, Spain aut Sigarreta José Faculdad de Matemáticas, Universidad Autónoma de Guerrero, Carlos E. Adame 5, Col. La Garita, Acapulco, Guerrero, Mexico aut Aequationes mathematicae Springer Basel 89/5(2015-10-01), 1311-1327 0001-9054 89:5<1311 2015 89 10 https://doi.org/10.1007/s00010-014-0324-0 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00010-014-0324-0 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Carballosa Walter Consejo Nacional de Ciencia y Tecnología (CONACYT) and Universidad Autónoma de Zacatecas, Paseo la Bufa, int. Calzada Solidaridad, 98060, Zacatecas, ZAC, Mexico aut NATIONALLICENCE 700 1- Rodríguez José Department of Mathematics, Universidad Carlos III de Madrid, Av. de la Universidad 30, 28911, Leganés, Madrid, Spain aut NATIONALLICENCE 700 1- Sigarreta José Faculdad de Matemáticas, Universidad Autónoma de Guerrero, Carlos E. Adame 5, Col. La Garita, Acapulco, Guerrero, Mexico aut NATIONALLICENCE 773 0- Aequationes mathematicae Springer Basel 89/5(2015-10-01), 1311-1327 0001-9054 89:5<1311 2015 89 10