There has been an upsurge of research on complex networks in recent years. The purpose this paper is to study the mathematical properties random pentagonal chain PE C n with help graph theory. Based id="M2"> , we first obtain expected value expressions Gutman in...

the first zagreb index $m_1$ of a graph $g$ is equal to the sum of squaresof degrees of the vertices of $g$. goubko proved that for trees with $n_1$pendent vertices, $m_1 geq 9,n_1-16$. we show how this result can beextended to hold for any connected graph with cyclomatic number $gamma geq 0$.in addition, graphs with $n$ vertices, $n_1$ pendent vertices, cyclomaticnumber $gamma$, and minimal $m...