On reverse degree distance of unicyclic graphs

Document Type : Research Paper


Northeast Normal University


The reverse degree distance of a connected graph $G$ is defined
in discrete mathematical chemistry as
r (G)=2(n-1)md-sum_{uin V(G)}d_G(u)D_G(u),
where $n$, $m$ and $d$ are the number of vertices, the number of
edges and the diameter of $G$, respectively, $d_G(u)$ is the degree of vertex $u$,
$D_G(u)$ is the sum of distance between vertex $u$ and all other vertices of $G$, and $V(G)$ is the vertex set of $G$.
determine the unicyclic graphs of given girth, number of pendant
vertices and maximum degree, respectively, with maximum reverse
degree distances. We also determine the
unicyclic graphs of given number of vertices, girth and diameter
with minimum degree distance.


Main Subjects