Teória grafov v chémii
The Estrada Index: An Updated Survey
The fundamental group and Galois coverings of hexagonal systems in 3-space.
The influence of symmetry on the probability of assembly pathways for icosahedral viral shells.
The irregularity of graphs under graph operations
The irregularity of a simple undirected graph G was defined by Albertson [5] as irr(G) = ∑uv∈E(G) |dG(u) − dG(v)|, where dG(u) denotes the degree of a vertex u ∈ V (G). In this paper we consider the irregularity of graphs under several graph operations including join, Cartesian product, direct product, strong product, corona product, lexicographic product, disjunction and sym- metric difference. We give exact expressions or (sharp) upper bounds on the irregularity of graphs under the above mentioned...
The stable roommates problem and chess tournament pairings.
The subalgebra lattice of a finite algebra
The aim of this paper is to characterize pairs (L, A), where L is a finite lattice and A a finite algebra, such that the subalgebra lattice of A is isomorphic to L. Next, necessary and sufficient conditions are found for pairs of finite algebras (of possibly distinct types) to have isomorphic subalgebra lattices. Both of these characterizations are particularly simple in the case of distributive subalgebra lattices. We do not restrict our attention to total algebras only, but we consider the more...
The Sun graph is determined by its signless Laplacian spectrum.
The Wiener number of Kneser graphs
The Wiener number of a graph G is defined as 1/2∑d(u,v), where u,v ∈ V(G), and d is the distance function on G. The Wiener number has important applications in chemistry. We determine the Wiener number of an important family of graphs, namely, the Kneser graphs.
The Wiener number of powers of the Mycielskian
The Wiener number of a graph G is defined as , d the distance function on G. The Wiener number has important applications in chemistry. We determine a formula for the Wiener number of an important graph family, namely, the Mycielskians μ(G) of graphs G. Using this, we show that for k ≥ 1, , where Sₙ, Tₙ and Pₙ denote a star, a general tree and a path on n vertices respectively. We also obtain Nordhaus-Gaddum type inequality for the Wiener number of .
Two operations of merging and splitting components in a chain graph
In this paper we study two operations of merging components in a chain graph, which appear to be elementary operations yielding an equivalent graph in the respective sense. At first, we recall basic results on the operation of feasible merging components, which is related to classic LWF (Lauritzen, Wermuth and Frydenberg) Markov equivalence of chain graphs. These results are used to get a graphical characterisation of factorisation equivalence of classic chain graphs. As another example of the use...