It is well known that the incorporation of wetting agents in drug solutions for local application enhances the penetration of the drug into the tissues (McKee et al., 1943; Bellows and Gutman, 1943; Trim and Alexander, 1946). Ginsburg and Robson (1945) have shown that when dodecyl sodium sulphate is incorporated in solutions of sodium sulphacetamide applied to the cornea, the increase in penetr...

Search engines are among the most popular and useful services on the web. Ingwersen and Järvelin (2005) recommend evaluating an IR system based on how much it helps the user achieve their task effectively and efficiently. Therefore, to evaluate a search engine holistically, the users’ rating of the results should be taken into account. Many previous studies have evaluated the effectiveness of w...

The energy of a graph was introduced by Gutman in 1978 as the sum of the absolute values of the eigenvalues of its adjacency matrix. We study the energy of integral circulant graphs, also called gcd graphs. These are Cayley graphs on cyclic groups (i.e. there adjacency matrix is circulant) each of whose eigenvalues is an integer. Given an arbitrary prime power p, we determine all integral circu...

Recently Nikolić, Trinajstić and Randić put forward a novel modification W(G) of the Wiener number W(G), called modified Wiener index , which definition was generalized later by Gutman and the present authors. Here we study another class of modified indices defined as Wmin,λ(G)=∑(V(G) mG(u,ν) −mG(u,ν) ) and show that some of the important properties of W(G), W(G) and W(G) are also properties of...

We study the point-to-point shortest path problem in a setting where preprocessing is allowed. We improve the reach-based approach of Gutman [16] in several ways. In particular, we introduce a bidirectional version of the algorithm that uses implicit lower bounds and we add shortcut arcs which reduce vertex reaches. Our modifications greatly reduce both preprocessing and query times. The result...

The principal investigators would like to thank their collaborators, research assistants and master students which were incorporated in the research project and essentially contribute to the planned assignments. These are the PhD students Wolfgang Bier (UniK), Ulrich Heisserer (TUM), and Magda Martins-Wagner (UniBW München) as well as the students Idit Cohen, Shachar Koen, and Alexander Ripp. F...

Suppose that G is a simple graph. We prove that if G contains a small number of cycles of even length then the matching polynomial of G can be expressed in terms of the characteristic polynomials of the skew adjacency matrix A(G) of an arbitrary orientation G of G and the minors of A(G). In addition to a formula previously discovered by Godsil and Gutman, we obtain a different formula for the m...

Several alternative definitions to graph energy have appeared in literature recently, the first among them being the Laplacian energy, defined by Gutman and Zhou in [Linear Algebra Appl. 414 (2006), 29–37]. We show here that Laplacian energy apparently has small power of discrimination among threshold graphs, by showing that, for each n, there exists a set of n mutually noncospectral connected ...

Cocycles are a key object in Antolín Camarena and Szegedy's theory of nilspaces. We introduce variants these cocycles, named nilcycles, enabling us to give conditions which guarantee that an ergodic group extension strictly distal system admits topological model. In particular we show if the base space is dynamical nilspace then model may be chosen for extension. This approach combined with str...

Let $G$ be a finite group. The intersection graph of is whose vertex set the all proper non-trivial subgroups and two distinct vertices $H$ $K$ are adjacent if only $H\cap K \neq \{e\}$, where $e$ identity group $G$. In this paper, we investigate some properties exploring topological indices such as Wiener, Hyper-Wiener, first second Zagreb, Schultz, Gutman eccentric connectivity $D_{2n}$ for $...