convex domination subdivision number of a graph

let $g=(v,e)$ be a simple graph. a set $dsubseteq v$ is adominating set of $g$ if every vertex in $vsetminus d$ has atleast one neighbor in $d$. the distance $d_g(u,v)$ between twovertices $u$ and $v$ is the length of a shortest $(u,v)$-path in$g$. an $(u,v)$-path of length $d_g(u,v)$ is called an$(u,v)$-geodesic. a set $xsubseteq v$ is convex in $g$ ifvertices from all $(a, b)$-geodesics belong to $x$ for any twovertices $a,bin x$. a set $x$ is a convex dominating set if it isconvex and dominating set. the {em convex domination number}$gamma_{rm con}(g)$ of a graph $g$ equals the minimumcardinality of a convex dominating set in $g$. {em the convexdomination subdivision number} sd$_{gamma_{rm con}}(g)$ is theminimum number of edges that must be subdivided (each edge in $g$can be subdivided at most once) in order to increase the convexdomination number. in this paper we initiate the study of convexdomination subdivision number and we establish upper bounds forit.