Slobodan K. Simić

The polynomial reconstruction of unicyclic graphs is unique

We consider the problem of reconstructing the characteristic polynomial of a graph G from its polynomial deck, i.e. the collection of characteristic polynomials of its vertex-deleted subgraphs. Here we provide a positive solution for all unicyclic graphs.

On graphs whose least eigenvalue is greater than –2

Graphs with least eigenvalue greater than or equal to are to a big extent studied by Hoffman and other authors from the early beginning of the spectral graph theory. Most of these results are summarized in the monograph [Cvetković D, Rowlinson P, Simić S. Spectral generalizations of line graphs, on graphs with least eigenvalue , Cambridge University Press, 2004], and the survey paper [Cvetković D, Rowlinson P, Simić S. Graphs with least eigenvalue : ten years on, Linear Algebra Appl. 2015;484:504–539] which is aimed to cover the next 10 years since their monograph appeared. Here, we add some further results. Among others, we identify graphs whose least eigenvalue is greater than , but closest to within the graphs of fixed order. Some consequences of these considerations are found in the context of the highest occupied molecular orbital–lowest unoccupied molecular orbital invariants.

Polynomial reconstruction of signed graphs whose least eigenvalue is close to -2

The polynomial reconstruction problem for simple graphs has been considered in the literature for more than forty years and is not yet resolved except for some special classes of graphs. Recently, the same problem has been put forward for signed graphs. Here, the reconstruction of the characteristic polynomial of signed graphs whose vertex-deleted subgraphs have least eigenvalue greater than

Signed line graphs with least eigenvalue - 2

-2

Fast algorithms for computing the characteristic polynomial of threshold and chain graphs

is considered.

Graph spectra in Computer Science

We use star complement technique to construct a basis for - 2 of signed line graphs using their root signed graphs. In other words, we offer a generalization of the corresponding results known in the literature for (unsigned) graphs in the context of line graphs and generalized line graphs.

On the Laplacian coefficients of signed graphs

Abstract The characteristic polynomial of a graph is the characteristic polynomial of its adjacency matrix. Finding efficient algorithms for computing characteristic polynomial of graphs is an active area of research and for some graph classes, like threshold graphs, there exist very fast algorithms which exploit combinatorial structure of the graphs. In this paper, we put forward some novel ideas based on divisor technique to obtain fast algorithms for computing the characteristic polynomial of threshold and chain graphs.