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 symmetric difference. ...

A tree T , in an edge-colored graph G, is called a rainbow tree if no two edges of T are assigned the same color. A k-rainbow coloring of G is an edge coloring of G having the property that for every set S of k vertices of G, there exists a rainbow tree T in G such that S ⊆ V (T ). The minimum number of colors needed in a k-rainbow coloring of G is the k-rainbow index of G, denoted by rxk(G). G...

This paper tries to outline a generic graph model as it can be used in ROR, to define requirements and framework conditions. It tries to summarize generic demands and to describe the query and functionality requirements that have to be satisfied by such databases. This paper presents basic ideas and the origin point of intended and starting database research projects and cooperation with univer...

In this partly expository paper we discuss and describe some of our old and recent results on partial orders on the set G n of graphs with n vertices and m edges and some operations on graphs within G n that are monotone with respect to these partial orders. The partial orders under consideration include those related with some Laplacian characteristics of graphs as well as with some probabilis...

Editorial Board Marat Arslanov, Kazan John T. Baldwin, Chicago, IL Douglas S. Bridges, Canterbury Armin Hemmerling, Greifswald Ramon Jansana, Barcelona Carl G. Jockusch, Urbana, IL Alexander Kechris, Pasadena, CA Ulrich Kohlenbach, Darmstadt H. Dugald Macpherson, Leeds Johann Makowsky, Haifa Andrzej Rosłanowski, Omaha, NE Jörg Rothe, Düsseldorf Wilfried Sieg, Pittsburgh, PA Stephen G. Simpson, ...

S is a local maximum stable set of G, and we write S 2 (G), if S is a maximum stable set of the subgraph induced by S [N(S), where N(S) is the neighborhood of S. Nemhauser and Trotter Jr. [5] proved that any S 2 (G) is a subset of a maximum stable set of G. In [1] we have proved that (G) is a greedoid for every forest G. The cases of bipartite graphs and triangle-free graphs were analyzed in [2...

Let d(G, k) be the number of pairs of vertices of a graph G that are at distance k, λ a real number, and Wλ(G) = ∑ k≥1 d(G, k)kλ. Wλ(G) is called the Wiener-type invariant of G associated to real number λ. In this paper, the Wiener-type invariants of some graph operations are computed. As immediate consequences, the formulae for reciprocal Wiener index, Harary index, hyperWiener index and Tratc...

The connection between certain entangled states and graphs has been heavily studied in the context of measurement-based quantum computation as a tool for understanding entanglement. Here we show that this correspondence can be harnessed in the reverse direction to yield a graph data structure which allows for more efficient manipulation and comparison of graphs than any possible classical struc...

The study of networks and graphs carried out by topological measures performs a vital role in securing their hidden topologies. This strategy has been extremely used biomedicine, cheminformatics bioinformatics, where computations dependent on graph invariants have made available to communicate the various challenging tasks. In quantitative structure–activity (QSAR) structure–property (QSPR) rel...

A graph G is said to be orderenergetic, if its energy equal order and it hypoenergetic less than order. Two non-isomorphic graphs of same are equienergetic their energies equal. In this paper, we construct some new families orderenergetic graphs, equiorderenergetic equihypoenergetic graphs.