For any integer $k\geq 3$ , we define sunlet graph of order $2k$, denoted by $L_{2k}$, as the consisting a cycle length $k$ together with pendant vertices, each adjacent to exactly one vertex cycle. In this paper, give necessary and sufficient conditions for existence $L_{8}$-decomposition tensor product wreath complete graphs.

Abstract A strong edge coloring of a graph G is proper such that every color class an induced matching. The minimum number colors required termed the chromatic index. In this paper we determine exact value index all unitary Cayley graphs. Our investigations reveal underlying product structure from which graphs emerge. We then go on to give tight bounds for Cartesian two trees, including formula...

This paper establishes a set of theorems that describe the diameter of a zero-divisor graph for a finite direct product R1 × R2 × · · · × Rn with respect to the diameters of the zero-divisor graphs of R1, R2, · · · , Rn−1 and Rn(n > 2).

We introduce the concept of neighborhood systems as a generalization of directed, reflexive graphs and show that the prime factorization of neighborhood systems with respect to the the direct product is unique under the condition that they satisfy an appropriate notion of thinness.

We construct a minimum cycle basis for the direct product K2 × Kp of two complete graphs where p ≥ 2. For p > 3, these bases consists only of squares. This completes the work of R. Hammack, who treated the case Kp ×Kq for p, q ≥ 3 [Inform. Process. Lett. 102 (2007), 214–218.]

For two normal edge-transitive Cayley graphs on groups H and K which have no common direct factor and gcd(|H/H ′|, |Z(K)|) = 1 = gcd(|K/K′|, |Z(H)|), we consider four standard products of them and it is proved that only tensor product of factors can be normal edge-transitive. c ⃝ 2014 IAUCTB. All rights reserved.

This paper presents a construction of a minimum cycle basis for the direct product of two complete graphs on three or more vertices. With the exception of two special cases, such bases consist entirely of triangles. © 2007 Elsevier B.V. All rights reserved.

a topological index of a molecular graph g is a numeric quantity related to g which isinvariant under symmetry properties of g. in this paper we obtain the randić, geometricarithmetic,first and second zagreb indices , first and second zagreb coindices of tensorproduct of two graphs and then the harary, schultz and modified schultz indices of tensorproduct of a graph g with complete graph of ord...

The main objective of this paper is to calculate the metric dimension and resolving-domination number zero-divisor graphs direct product finite fields. Let $F_1, \ldots, F_n(n \geqslant 2)$ be We consider graph $\Gamma(R)$ ring $R=F_1 \times \cdots F_n$ $(n determine $\beta(\Gamma(R))$ $\gamma_r(\Gamma(R))$ If order each field two, then we prove that $\beta(\Gamma(R)) \leqslant n-1$ $\gamma_r(\...

This study attempted to systematically inspect the impact of direct and indirect corrective feedbacks on the writing ability of EFL learners when using product/process based instructions. To do so, 110 female EFL learners, between the ages of 15 and 18, were randomly assigned into four experimental groups to receive four different kinds of treatments, namely product-based instruction with direc...