{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:39Z","timestamp":1753893819633,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>If X is a geodesic metric space and $x_1,x_2,x_3\\in X$, a\u00a0geodesic triangle $T=\\{x_1,x_2,x_3\\}$ is the union of the three\u00a0geodesics $[x_1x_2]$, $[x_2x_3]$ and $[x_3x_1]$ in $X$. The space\u00a0$X$ is $\\delta$-hyperbolic $($in the Gromov sense$)$ if any side\u00a0of $T$ is contained in a $\\delta$-neighborhood of the union of the two\u00a0other sides, for every geodesic triangle $T$ in $X$.\u00a0If $X$ is hyperbolic, we denote by\u00a0$\\delta (X)$ the sharp hyperbolicity constant of $X$, i.e.,\u00a0$\\delta (X)=\\inf\\{\\delta\\geq 0: \\, X \\, \\text{ is $\\delta$-hyperbolic}\\,\\}\\,.$\u00a0In this paper we characterize the strong product of two graphs $G_1\\boxtimes G_2$ which are hyperbolic,\u00a0in terms of $G_1$ and $G_2$:\u00a0the strong product graph $G_1\\boxtimes G_2$ is hyperbolic if and only if one of the factors is hyperbolic\u00a0and the other one is bounded.\u00a0We also prove some sharp relations between $\\delta (G_1\\boxtimes G_2)$, $\\delta (G_1)$, $\\delta (G_2)$ and the diameters of $G_1$ and $G_2$\u00a0(and we find families of graphs for which the inequalities are attained).\u00a0Furthermore, we obtain the exact values of the hyperbolicity constant for many\u00a0strong product graphs.<\/jats:p>","DOI":"10.37236\/3271","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T01:24:26Z","timestamp":1578705866000},"source":"Crossref","is-referenced-by-count":11,"title":["Gromov Hyperbolicity in Strong Product Graphs"],"prefix":"10.37236","volume":"20","author":[{"given":"Walter","family":"Carballosa","sequence":"first","affiliation":[]},{"given":"Roc\u00edo M.","family":"Casablanca","sequence":"additional","affiliation":[]},{"given":"Amauris","family":"De la Cruz","sequence":"additional","affiliation":[]},{"given":"Jos\u00e9 M.","family":"Rodr\u00edguez","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2013,7,19]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i3p2\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i3p2\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T11:16:40Z","timestamp":1579259800000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v20i3p2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,7,19]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2013,7,19]]}},"URL":"https:\/\/doi.org\/10.37236\/3271","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2013,7,19]]},"article-number":"P2"}}