a $(p,q)$ graph $g$ is said to have a $k$-odd mean
labeling $(k ge 1)$ if there exists an injection $f : v
to {0, 1, 2, ldots, 2k + 2q - 3}$ such that the
induced map $f^*$ defined on $e$ by $f^*(uv) =
leftlceil frac{f(u)+f(v)}{2}rightrceil$ is a
bijection from $e$ to ${2k - 1, 2k + 1, 2k + 3, ldots, 2
k + 2q - 3}$. a graph that admits $k$...
