INDEPENDENT AND VERTEX COVERING NUMBER ON KRONECKER PRODUCT OF $C_n$
Thanin Sitthiwirattham, Jarunee Soontharanon · International Journal of Pure and Apllied Mathematics · 2011
Let α(G) and β(G) be the independent number and vertex covering number of G, respectively. The Kronecker Product G1 ⊗ G2 of graph of G1 and G2 has vertex set V (G1 ⊗ G2 )= V (G1) × V (G2) and edge set E(G1 ⊗ G2 )= {(u1v1)(u2v2)|u1u2 ∈ E(G1) and v1v2 ∈ E(G2)}. In this paper, let G is a simple graph with order p, we prove that, α(Km,n ⊗G)= max {(m+n)α(G),p max{m, n}} and β(Km,n ⊗G) =min {(m + n)β(G) ,p min{m, n}}. Mathematics Subject Classification: 05C69 , 05C70 , 05C76