In order to identify the CORRELATIONs and relationships between different traits in the bread wheat, 30 genotypes were investigated as sub-factors under the split plot experiment in the completely randomized design in greenhouse and the randomized complete block design in the field with three replications under the normal irrigation and post-anthesis water stress conditions. The results of the canonical CORRELATION analysis showed that at both normal and moisture stress levels, there was a significant CORRELATION between the pair of canonical variables obtained from the phenological traits and the yield components. Under the normal conditions in the greenhouse, to increase the spike density and length, the number of days to 50% flowering can be considered as a suitable selection criterion. According to the results of canonical CORRELATION analysis, under the stressed conditions in greenhouse, to increase the spike length, the number of days to the heading, maturity and 50% of flowering were among the important and effective factors. Under the optimum irrigation conditions in the field, the number of days to maturity was considered as one of the factors influencing the seed weight per spike. The results of canonical CORRELATION analysis under the field stress conditions showed that to increase the 1000-seed weight, the number of days to maturity can be considered an appropriate selection criterion.

Recently, E. Macajova and M. Skoviera proved that every bidirected Eulerian graph which admits a nowhere zero flow, admits a nowhere zero 4-flow. This result shows the validity of Bouchet's nowhere zero conjecture for Eulerian bidirected GRAPHS. In this paper we prove the same theorem in a different terminology and with a short and simple proof. More precisely, we prove that every Eulerian undirected graph which admits a zero-sum flow, admits a zero-sum 4-flow. As a conclusion we obtain a shorter proof for the previously mentioned result of Macajova and Skoviera.

We determine the forbidden induced subGRAPHS for the intersection of the classes of chordal bipartite GRAPHS and line GRAPHS of acyclic directed GRAPHS. This is a first step towards finding the forbidden induced subGRAPHS for the class of line GRAPHS of directed GRAPHS.

A set W ,V (G) is called a resolving set, if for every two distinct vertices u,v 2 V (G) there exists w 2 W such that d(u, w) 6= d(v, w), where d(x,y) is the distance between the vertices x and y. A resolving set for G with minimum cardinality is called a metric basis. A graph with a unique metric basis is called a uniquely dimensional graph. In this paper, we establish a family of graph called Solis graph, and we prove that if G is a minimal edge unique base graph with the base of size two, then G belongs to the Solis GRAPHS family. Finally, an algorithm is given for , nding the metric dimension of a Solis graph.

The Hosoya index $Z(G)$ of a graph $G$ is the total number of matchings in it. In this paper, the recursive formulas of the Hosoya index of semitotal graph $Q(G)$ and total graph $T(G)$ for certain GRAPHS $G$ are obtained. Moreover, we obtain the bounds of the Hosoya index of semitotal and total GRAPHS of a connected graph $G$.

In this paper we prove that any distance-balanced graph G with D (G) ³|V (G)| -3 is regular. Also we define notion of distance- balanced closure of a graph and we find distance-balanced closures of trees T with D (T) ³ |V (T)| -3.

Let $t_p(G)$ denote the number of paths in a graph $G$ and let $f:E\rightarrow \mathbb{Z}^+$ be an edge labeling of $G$. The weight of a path $P$ is the sum of the labels assigned to the edges of $P$. If the set of weights of the paths in $G$ is $\{1,2,3,\dots,t_p(G)\}$, then $f$ is called a Leech labeling of $G$ and a graph which admits a Leech labeling is called a Leech graph. In this paper, we prove that the complete bipartite GRAPHS $K_{2,n}$ and $K_{3,n}$ are not Leech GRAPHS and determine the maximum possible value that can be given to an edge in the Leech labeling of a cycle.