An independent broadcast on a connected graph $G$is a function $f:V(G)to mathbb{N}_0$such that, for every vertex $x$ of $G$, the value $f(x)$ is at most the eccentricity of $x$ in $G$,and $f(x)>0$ implies that $f(y)=0$ for every vertex $y$ of $G$ within distance at most $f(x)$ from $x$.The broadcast independence number $alpha_b(G)$ of $G$is the largest weight $sumlimits_{xin V(G)}f(x)$of an ind...

The objective of the present paper is to study maximum radius r a connected graph order n, minimum degree δ ≥ 2 and girth at least g 4. Erdős, Pach, Pollack Tuza proved that if = 4, is, triangle-free, then ≤ n − + 12, noted up value additive constant, this upper bound tight. In we shall determine exact maximum. For larger values little known. We settle for 6 , 8 prove an every even g, which con...