in this research, the effect of temperature on the physical and chemical behavior of nylon 66 tire cords in the range of 50-200°c and 16 h testing was studied. the results showed that heat treatment considerably reduced the breaking strength of cords. the intensity of reduction of breaking strength below 100°c and above 120°c was more pronounced than intermediate temperatures. the changes in pr...

a set $s$ of vertices in a graph $g=(v,e)$ is called a total$k$-distance dominating set if every vertex in $v$ is withindistance $k$ of a vertex in $s$. a graph $g$ is total $k$-distancedomination-critical if $gamma_{t}^{k} (g - x) < gamma_{t}^{k}(g)$ for any vertex $xin v(g)$. in this paper,we investigate some results on total $k$-distance domination-critical of graphs.

The chromatic sum of a graph G, ∑ (G), is introduced in the dissertation of Kubicka [3]. It is defined as the smallest possible total over all vertices that can occur among all colorings of G using natural numbers for the colors. It is known that computing the chromatic sum of an arbitrary graph is an NP-complete problem. The vertex-strength of the graph G, denoted by s(G), is the smallest inte...

In this paper, we introduce the notions of product vague graph, balanced product vague graph, irregularity and total irregularity of any irregular vague graphs and some results are presented. Also, density and balanced irregular vague graphs are discussed and some of their properties are established. Finally we give an application of vague digraphs.

Karoński, Luczak, and Thomason (2004) conjectured that, for any connected graph G on at least three vertices, there exists an edge weighting from {1, 2, 3} such that adjacent vertices receive different sums of incident edge weights. Bartnicki, Grytczuk, and Niwcyk (2009) made a stronger conjecture, that each edge’s weight may be chosen from an arbitrary list of size 3 rather than {1, 2, 3}. We ...

&lt;abstract&gt;&lt;p&gt;We introduce the general Albertson irregularity index of a connected graph $ G and define it as A_{p}(G) = (\sum_{uv\in E(G)}|d(u)-d(v)|^p)^{\frac{1}{p}} $, where p is positive real number d(v) degree vertex v in $. The new not only generalization well-known \sigma $-index, but also Minkowski norm vertex. We present lower upper bounds on index. In addition, we study ext...