The support of a matrix M is the (0, 1)-matrix with ij-th entry equal to 1 if the ij-th entry of M is non-zero, and equal to 0, otherwise. The digraph whose adjacency matrix is the support of M is said to be the digraph of M . This paper observes some structural properties of digraphs and Cayley digraphs, of unitary matrices. We prove that a group generated by two elements has a set of generato...

Let D be a digraph, V (D) and A(D) will denote the sets of vertices and arcs of D, respectively. A kernel N of D is an independent set of vertices such that for every w∈V (D) − N there exists an arc from w to N . A digraph D is called right-pretransitive (resp. left-pretransitive) when (u; v)∈A(D) and (v; w)∈A(D) implies (u; w)∈A(D) or (w; v)∈A(D) (resp. (u; v)∈A(D) and (v; w)∈A(D) implies (u; ...

A digraph obtained by replacing each edge of a complete n-partite graph by an arc or a pair of mutually opposite arcs is called a semicomplete n-partite digraph. We call (D)=max16 i6 n{|Vi|} the independence number of the semicomplete n-partite digraph D, where V1; V2; : : : ; Vn are the partite sets of D. Let p and c, respectively, denote the number of vertices in a longest directed path and t...

An m-colored digraph is a digraph whose arcs are colored with m colors. A directed path is monochromatic when its arcs are colored alike. A set S ⊆ V (D) is a kernel by monochromatic paths whenever the two following conditions hold: 1. For any x, y ∈ S, x 6= y, there is no monochromatic directed path between them. 2. For each z ∈ (V (D)− S) there exists a zS-monochromatic directed path. In this...

A digraph obtained by replacing each edge of a complete p-partite graph by an arc or a pair of mutually opposite arcs with the same end vertices is called a semicom-plete p-partite digraph, or just a semicomplete multipartite digraph. A semicomplete multipartite digraph with no cycle of length two is a multipartite tournament. In a digraph D, an r-king is a vertex q such that every vertex in D ...

A kernel N of a digraph D is an independent set of vertices of D such that for every w ∈ V (D)− N there exists an arc from w to N . If every induced subdigraph of D has a kernel, D is said to be a kernel perfect digraph. D is called a critical kernel imperfect digraph when D has no kernel but every proper induced subdigraph of D has a kernel. If F is a set of arcs of D, a semikernel modulo F of...

A new test sequence generation method is proposed for testing the conformance of a protocol implementation to its data portion modeled by an Extended Finite State Machine (EFSM), which is represented by a Data Flow Digraph. All-Use and IO-dfchain are two important criteria for selecting paths from the Data Flow Digraph to generate a test sequence which traces the data flow property, but it is a...

For digraphs D and H , a mapping f : V (D)→V (H) is a homomorphism of D to H if uv ∈ A(D) implies f(u)f(v) ∈ A(H). For a fixed digraph H , the homomorphism problem is to decide whether an input digraph D admits a homomorphism to H or not, and is denoted as HOM(H). An optimization version of the homomorphism problem was motivated by a realworld problem in defence logistics and was introduced in ...

A kernel of a digraph is a set of vertices which is both independent and absorbant. Let D be a digraph such that every proper induced subdigraph has a kernel. If D has a kernel, then D is kernel perfect, otherwise D is critical kernel-imperfect (for short CKI-digraph). In this work we prove that if a CKI-digraph D is not 2-arc connected, then D − a is kernel perfect for any bridge a of D. If D ...

Let G be a digraph, LG its line digraph and A(G) and A(LG) their adjacency matrices. We present relations between the Jordan Normal Form of these two matrices. Besides, we study the spectra of those matrices and obtain a relationship between their characteristic polynomials that allows to relate properties of G and LG regarding the number of cycles of a given length.