A chord is an edge between two vertices of a cycle that is not an edge on the cycle. If a cycle has at least one chord, then the cycle is called a chorded cycle, and if a cycle has at least two chords, then the cycle is called a doubly chorded cycle. The minimum degree and the minimum degree-sum conditions are given for a graph to contain vertex-disjoint chorded (doubly chorded) cycles containi...

A cycle C in a graph G is dominating if every edge of G is incident with at least one vertex of C. For a set H of connected graphs, a graph G is said to be H-free if G does not contain any member of H as an induced subgraph. When |H| = 2, H is called a forbidden pair. In this paper, we investigate the characterization of the class of the forbidden pairs guaranteeing the existence of a dominatin...

We consider the problem of computing a minimum cycle basis in a directed graph G. The input to this problem is a directed graph whose arcs have positive weights. In this problem a 1 0 1 incidence vector is associated with each cycle and the vector space over generated by these vectors is the cycle space of G. A set of cycles is called a cycle basis of G if it forms a basis for its cycle space. ...