The imbalance of an edge e = {u, v} in a graph is defined as i(e) = |d(u)−d(v)|, where d(·) is the vertex degree. The irregularity I(G) of G is then defined as the sum of imbalances over all edges of G. This concept was introduced by Albertson who proved that I(G)\leqslant 4n^{3}/27 (where n = |V(G)|) and obtained stronger bounds for bipartite and triangle-free graphs. Since then a number of additional bounds were given by various authors. In this paper we prove a new upper bound, which improves a bound found by Zhou and Luo in 2008. Our bound involves the Laplacian spectral radius λ., Felix Goldberg., and Obsahuje seznam literatury
The present article aims at reviewing the debate on the impact which international courtsand quasi-judicial bodies have on the contemporary international relations. This impact is now aptly describedin terms of judicialization of international relations. Building upon data from the previously publishedstudies, the article identifies both legal and extralegal factors which stand behind the process of judicializationof international relations. On the other hand, while there is no doubt this process has reachedunprecedented extent, its degree is not equal in the contemporary world. The recourse to judicial settlementof international disputes is frequent indeed in Europe, however, this is not necessarily true of the other regions.Moreover, it seems that even in the era of judicialization of international relations, the willingness to bringdisputes before international courts and quasi-judicial bodies is overwhelmingly, albeit not exclusively, reservedto several distinct categories of disputes, especially those which stem from international economic relations.Purely political disputes are judicially settled with much bigger caution. Therefore, it seems correctto conclude that international courts and quasi-judicial bodies play non-negligible role in the contemporaryinternational relations but, for the time being, they do not definitely constitute world government, as it issometimes suggested.
A graph $G$ is a minimal claw-free graph (m.c.f. graph) if it contains no $K_{1,3}$ (claw) as an induced subgraph and if, for each edge $e$ of $G$, $G-e$ contains an induced claw. We investigate properties of m.c.f. graphs, establish sharp bounds on their orders and the degrees of their vertices, and characterize graphs which have m.c.f. line graphs.
The aim of the paper is to investigate the structure of disjoint iteration groups on the unit circle ${\mathbb{S}^1}$, that is, families ${\mathcal F}=\lbrace F^{v}\:{\mathbb{S}^1}\longrightarrow {\mathbb{S}^1}\; v\in V\rbrace $ of homeomorphisms such that
\[ F^{v_{1}}\circ F^{v_{2}}=F^{v_{1}+v_{2}},\quad v_1, v_2\in V, \] and each $F^{v}$ either is the identity mapping or has no fixed point ($(V, +)$ is an arbitrary $2$-divisible nontrivial (i.e., $\mathop {\mathrm card}V>1$) abelian group).