1-edge contraction: total vertex stress and confluence number

This paper introduces certain relations between $1$-edge contraction and the total vertex stress and the confluence number of a graph. a main result states that if a graph $g$ with $zeta(g)=kgeq 2$ has an edge $v_iv_j$ and a $zeta$-set $mathcal{c}_g$ such that $v_i,v_jin mathcal{c}_g$ then, $zeta(g/v_iv_j) = k-1$. in general, either $mathcal{s}(g/e_i) leq mathcal{s}(g/e_j)$ or $mathcal{s}(g/e_j) leq mathcal{s}(g/e_i)$ is true. this observation leads to an investigation into the question: for which edge(s) $e_i$ will $mathcal{s}(g/e_i) = max{mathcal{s}(g/e_j):e_j in e(g)}$ and for which edge(s) will $mathcal{s}(g/e_j) = min{mathcal{s}(g/e_ell):e_ell in e(g)}$?