Maximum genus and maximum nonseparating independent set of a 3-regular graph

Yuangqiu Huang, Yanpei Liu
1997 Discrete Mathematics  
A set J C V is called a nonseparating independent set (nsis) of a connected graph G = (V, E), if J is an independent set of G, i.e., E A {uv [ Vu, v E J} = 0, and G -J is connected. We call z(G) = maxJ{lJ[ tJ is an nsis of G} the nsis number of G. Let G be a 3-regular connected graph; we prove that the maximum genus, denoted by 7M(G), of G is equal to z(G). Then, according to this result, some new characterizations of the maximum genus 7M(G) are obtained.
doi:10.1016/s0012-365x(96)00299-3 fatcat:hkjjwc6lzndtxlt27fgtexmkuq