TOWARDS A SPECTRAL THEORY OF GRAPHS BASED ON THE SIGNLESS LAPLACIAN, III
Page 1 Applicable Analysis and Discrete Mathematics available online at http://pefmath.etf.rs …

Let K q, C q and P q denote the complete graph, the cycle and the path with q vertices,
respectively. We use Q (G) to denote the signless Laplacian matrix of a simple undirected …

We investigate when a complete graph K n with some edges deleted is determined by its
adjacency spectrum. It is shown to be the case if the deleted edges form a matching, a …

For a graph G, the first Zagreb index is defined as the sum of the squares of the vertices
degrees. By investigating the connection between the first Zagreb index and the first three …

A graph is said to be DLS, if there is no other non-isomorphic graph with the same Laplacian
spectrum. Let G be a DLS graph. We show that G× Kr is DLS if G is disconnected. If G is …

A graph is determined by its signless Laplacian spectrum if no other nonisomorphic graph
has the same signless Laplacian spectrum (simply G is DQS). Let T (a, b, c) denote the T …

The Laplacian spectrum of a graph consists of the eigenvalues (together with multiplicities)
of the Laplacian matrix. In this article we determine, among the graphs consisting of disjoint …

A Π-shape tree is a tree with exactly two of its vertices having the maximum degree 3. In this
article, we classify the Π-shape trees into six types according to the number of their closed …

For two disjoint graphs G and H, the join of G and H, denoted by G∨ H, is the graph
obtained from G∪ H by joining each vertex of G to each vertex of H. A graph is said to be …

We consider the problem of reconstructing the characteristic polynomial of a signed graph
from the collection of characteristic polynomials of its vertex-deleted subgraphs. We resolve …