A k-edge colouring (not necessarily proper) of a graph with colours in {1,2,…,k} is neighbour sum distinguishing if, for any two adjacent vertices, the sums edges incident each them are distinct. The smallest value k such that G exists denoted by χ∑e(G). When we add additional restriction must be proper, then χ∑′(G). Such colourings studied on connected at least 3 vertices. There famous conject...

Let G be a finite group and let Irr(G) the set of all irreducible complex characters G. For character χ∈Irr(G), number cod(χ):=|G:ker(χ)|/χ(1) is called co-degree χ. The co-degrees denoted by cod(G). In this paper, we show that for nontrivial G, |Irr(G)|=|cod(G)| if only isomorphic to Z2 or S3.

A class of graphs is hereditary if it is closed under isomorphism and induced subgraphs. A class G of graphs is χ-bounded if there exists a function f : N → N such that for all graphs G ∈ G, and all induced subgraphs H of G, we have that χ(H) ≤ f(ω(H)). We prove that proper homogeneous sets, clique-cutsets, and amalgams together preserve χ-boundedness. More precisely, we show that if G and G∗ a...

background: to compare mental health and well- being in different levels of the perceived discrimination among iranian people living in tehran. method: using multi- stage sampling, 1255 subjects with the average age of 45 years and 9 months (including 672 women and 583 men) were selected and they completed all items of the general health questionnaire (ghq), the social well- being inventory (sw...

The language χ is a modeling and simulation language which is currently mainly used to analyse and optimize the performance of industrial systems. To be able to also verify functional properties of a system using a χ model, part of the language has been given a formal semantics. Rather than implementing a new model checker for χ, the philosophy is to provide automatic translations from χ into t...