The type of bonding present in a substance with these properties high melting point, brittleness, and conducting electricity when dissolved in water is ionic bonding. Ionic bonds form between metal and non-metal elements, where electrons are transferred from the metal to the non-metal, creating charged ions that are attracted to each other. These substances typically have high melting points, are brittle in their solid state, and conduct electricity when dissolved in water due to the presence of mobile ions.