The degree distance of a connected graph $G$ with vertex set $V(G)$ is defined as $D^\prime(G)=\sum_{u\in V(G)}d_G(u)D_G(u)$, where $d_G(u)$ is the degree of vertex $u$ and $D_G(u)$ is the sum of distances between $u$ and all remaining vertices of $G$. The authors provide upper bounds for maximum degree distances in the class of connected graphs with exactly two cycles. It is showed that the obtained bounds are sharp. The proof is split into two parts: for graphs with two disjoint cycles and graphs with two cycles sharing a common vertex.
Reviewer: Gabriel Semanisin (Kosice)