We show that the diameter of connected $k$-colorable graphs with minimum degree $\geq \delta$ and order $n$ is at most $\left(3-\frac{1}{k-1}\right)\frac{n}{\delta}-1$, while for $k=3$, it $\frac{57n}{23\delta}+O\left(1\right)$.

Erdős et al. made conjectures for the maximum diameter of connected graphs without a complete subgraph K k + 1 ${K}_{k+1}$ , which have order n $n$ and minimum degree δ $\delta $ . Settling weaker version problem, by strengthening -free condition to $k$ -colorable, we solve problem = 3 $k=3$ 4 $k=4$ using unified linear programming duality approach. The case is substantial simplification result...

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 ...