independence number and connectivity of maximal connected domination vertex critical graphs

A κ-cec graph is a graph g which has connected domination numberc(g) = κ and c(g+uv) < κ for every uv 2 e(g). a κ-cvc graph g is a 2-connectedgraph with c(g) = k and γc(g - v) < k for any v 2 v (g). a graph is said to bemaximal κ-cvc if it is both k-cec and k-cvc. let δ, κ, and α be the minimumdegree, connectivity, and independence number of g, respectively. in this work, weprove that for a maximal 3-cvc graph, if α = κ, then κ = δ. we additionally considerthe class of maximal 3-cvc graphs with α < κ and κ < δ, and prove that every3-connected maximal 3-cvc graph when κ < δ is hamiltonian connected.