(5pts) Clearly state for what values of n ≥ 1 is there a simple 3-regular graph...

Solution (a) NOW Noco of n2) Calculating Calculating the coalues The values of nzl por which is exist a 3-regular goaph is no $4,6,8 ... & i.e.) In24 and niss even know Odd degree vertices of a graph & even cand inality they 3- regular graph ieg graph where each yeotex baş degree 3 most have even number of vertices, but in case of & vester graphs it can at most have degree, thus the claim holds. © El we know that) & dco) = 2 Here JE = cand i nality of Cope seti LEV all the bertices have degree do - degree of vertale IVI = condina ity of Vertex set 3N - Q1E) JET = 3n complete Thus, n must be even. But if na then IE1=3 but a verter graph can have at most E1=1 graphs exist for not and Therefore, where 3-regular nis even. csca Scanned With CamScanner