en تخصصي Special پژوهشي Research paper <p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;">Let $G$ be a connected graph on $n$ vertices. $G$ is called tricyclic if it has $n + 2$ edges, and tetracyclic if $G$ has exactly $n + 3$ edges. Suppose $mathcal{C}_n$ and $mathcal{D}_n$ denote the set of all tricyclic and tetracyclic $n-$vertex graphs, respectively. The aim of this paper is to calculate the minimum and maximum of eccentric connectivity index in $mathcal{C}_n$ and $mathcal{D}_n$.</p> Tricyclic graph, Tetracyclic graph, Eccentric connectivity index 137 143 http://ijmsi.ir/browse.php?a_code=A-10-1873-2&slc_lang=en&sid=1 M. Tavakoli M.tavakoly@Alumni.ut.ac.ir 10031947532846002925 10031947532846002925 No Ferdowsi University of Mashhad F. Rahbarnia rahbarnia@um.ac.ir 10031947532846002926 10031947532846002926 No Ferdowsi University of Mashhad A. R Ashrafi ashrafi@kashanu.ac.ir 10031947532846002927 10031947532846002927 Yes University of Kashan