Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X39420130901On reverse degree distance of unicyclic graphs681706437ENZ.DuNortheast Normal UniversityB.ZhouNortheast Normal UniversityJournal Article20111025The reverse degree distance of a connected graph $G$ is defined <br />in discrete mathematical chemistry as <br />[ <br />r (G)=2(n-1)md-sum_{uin V(G)}d_G(u)D_G(u), <br />] <br />where $n$, $m$ and $d$ are the number of vertices, the number of <br />edges and the diameter of $G$, respectively, $d_G(u)$ is the degree of vertex $u$, <br /> $D_G(u)$ is the sum of distance between vertex $u$ and all other vertices of $G$, and $V(G)$ is the vertex set of $G$. <br />We <br />determine the unicyclic graphs of given girth, number of pendant <br />vertices and maximum degree, respectively, with maximum reverse <br />degree distances. We also determine the <br />unicyclic graphs of given number of vertices, girth and diameter <br />with minimum degree distance.http://bims.iranjournals.ir/article_437_7a694edd090f25ab56c01b6e0653732b.pdf