Bounds on the Structural Indices of Primitive Non-powerful Generalized Sign Pattern Matrices

In view of the special effects of "loop" in the study of structural index problems, two classes of special generalized signed digraphs are defined: primitive non-powerful generalized signed digraphs with intersecting cycles structure and that with distinguished intersecting cycles structure, respectively. With restriction on primitive non-powerful generalized signed digraphs with intersecting cycles structure and those with distinguished intersecting cycles structure, upper bounds on the structural indices, e.g. kth local τ-base, kth same τ-base, kth lower τ-base, kth upper τ-base and ω-indecomposable base, are discussed by imitating the digraphs, analyzing the ambiguous reachable set and using the properties of Frobenius numbers, respectively.