Szeged Fragmental Indices

Novel Szeged indices, defined on unsymmetric matrices, which collect various fragmental topological properties, are proposed. They are illustrated on selected graphs possessing heteroatoms, multiple bonds and stereoisomers. Correlations on organic structures with herbicidal activity and explosive properties support the usefulness of these newly proposed indices

The vertex PI index and Szeged index of bridge graphs

AbstractRecently the vertex Padmakar–Ivan (PIv) index of a graph G was introduced as the sum over all edges e=uv of G of the number of vertices which are not equidistant to the vertices u and v. In this paper the vertex PI index and Szeged index of bridge graphs are determined. Using these formulas, the vertex PI indices and Szeged indices of several graphs are computed

Computing the Szeged and PI Indices of VC5C7[p,q] and HC5C7[p,q] Nanotubes

In this paper we give a GAP program for computing the Szeged and the PI indices of any graph. Also we compute the Szeged and PI indices of VC5C7 [ p,q] and HC5C7 [ p,q] nanotubes by this program

The Fredholm index of locally compact band-dominated operators on Lp(R)L^p (R)

We establish a necessary and sufficient criterion for the Fredholmness of a general locally compact band-dominated operator $A$ on $L^p(R)$ and solve the long-standing problem of computing its Fredholm index in terms of the limit operators of $A$. The results are applied to operators of convolution type with almost periodic symbol