CONNECTIVITY AND SOME OTHER PROPERTIES OF GENERALIZED SIERPINSKI GRAPHS

If G is a graph and n a positive integer, then the generalized Sierpinski graph S-G(n) is a fractal-like graph that uses G as a building block. The construction of S-G(n) generalizes the classical Sierpinski graphs S-p(n), where the role of G is played by the complete graph K-p. An explicit formula for the number of connected components in S(G)(n )is given and it is proved that the (edge-)connectivity of S-G(n) equals the (edge-)connectivity of G. It is demonstrated that S-G(n) contains a 1-factor if and only if S-G(n) contains a 1-factor. Hamiltonicity of generalized Sierpinski graphs is also discussed.