On C-Perfection of Tensor Product of Graphs

A graph G is C-perfect if, for each induced subgraph H in G, the induced cycle independence number of H is equal to its induced cycle covering number. Here, the induced cycle independence number of a graph G is the cardinality of the largest vertex subset of G, whose elements do not share a common induced cycle, and induced cycle covering number is the minimum number of induced cycles in G that covers the vertex set of G. C-perfect graphs are characterized as series-parallel graphs that do not contain any induced subdivisions of K-2,K-3, in literature. They are also isomorphic to the class of graphs that has an JoY-tree. In this article, we examine the C-perfection of tensor product of graphs, also called direct product or Kronecker product. The structural properties of C-perfect tensor product of graphs are studied. Further, a characterization for C-perfect tensor product of graphs is obtained.