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## Connected Domination Number and a New Invariant in Graphs with Independence Number Three

Keywords: dominating set, number of Hadwiger, clique number, independence number.

### Abstract

Adding a connected dominating set of vertices to a graph $G$ increases its number of Hadwiger $h(G)$. Based on this obvious property in [2] we introduced a new invariant $\eta(G)$ for which $\eta(G)\leq h(G)$. We continue to study its property. For a graph $G$ with independence number three without induced chordless cycles $C_7$ and with $n(G)$ vertices, $\eta(G)\geq n(G)/4$.

Department of Mathematics
CUNY Borough of Manhattan Community College
199 Chambers St, New York, NY 10007, USA
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