The Independence Graph Ind(G) of a Graph G is the Graph with vertices as maximum independent sets of G and two vertices are adjacent, if and only if the corresponding maximum independent sets are disjoint. In this work, we find the Independence Graph of Cartesian product of d copies of complete Graphs Kq, which is known as the Hamming Graph H(d, q). Greenwell and Lovasz [7] found that the Independence number of direct product of d copies of Kq as qd−1. We prove that the Independence number of Hamming Graph H(d, q), which is cartesian product of d copies of Kq, is also qd−1. As an application of our findings, we find answers for rook problem in higher dimensional square chess board.

A distinguishing coloring of a simple Graph $G$ is a vertex coloring of $G$ which is preserved only by the identity automorphism of $G$. In other words, this coloring ``breaks'' all symmetries of $G$. The distinguishing number $D(G)$ of a Graph $G$ is defined to be the smallest number of colors in a distinguishing coloring of $G$. This concept of “symmetry breaking” was first proposed by Babai in 1977 and after the publication of a seminal paper by Albertson in 1996, it attracted the attention of many mathematicians. In this paper, along with studying some relations between $D(G)$ and some other important Graph parameters, we introduce the concept of a $(D,\alpha)$-ordinary Graph which displays the comparison between $D(G)$ and the Independence number $\alpha(G)$. Then we consider the classification of $(D,\alpha)$-ordinary Graphs in various families of Graphs such as forests, cycles, generalized Johnson Graphs, Cartesian products of Graphs and line Graphs of connected claw-free Graphs. We also propose some conjectures and discuss about some future research directions in this topic.

There are many diff, erent Graphs one can associate to a group. Some examples are the wellknown Cayley Graph, the zero divisor Graph (of a ring), the power Graph, and the recently introduced coprime Graph of a group. The coprime Graph of a group G, denoted G, is the Graph whose vertices are the group elements with g adjacent to h if and only if (o(g),o(h)) = 1. In this paper we calculate the Independence number of the coprime Graph of the dihedral groups. Additionally, we characterize the groups whose coprime Graph is perfect.

Recently, some techniques such as adding whiskers and attaching Graphs to vertices of a given Graph, have been proposed for constructing a new vertex decomposable Graph. In this paper, we present a new method for constructing vertex decomposable Graphs. Then we use this construction to generalize the result due to Cook and Nagel.

In this paper, we find the star chromatic number of central Graph of complete bipartite Graph and corona Graph of complete Graph with path and cycle.

The World Association of Medical Editors defines editorial Independence as: full control over the editorial content of the journal, regardless of conflicts with the commercial success of the publication or the owners interests.(1) Fortunately, our Editorial Advisory Board recently met to discuss this issue. Separation of the editorial decisions from financial issues is essential to ensure editorial Independence. There are outright threats to continued editorial Independence. We reaffirm the core value of editorial freedom. The Committee on Publication Ethics has published a draft code of conduct for medical editors proposing a framework in detail for the relationship between the journal editors and the owners.(2) The role of the editors is to ensure accuracy of the material published for which they have to rely on the authors as well as an efficient review process. Authors should submit the ethical clearance or approval by the ethics committee for any research work. However, the editor is still responsible for checking out if there is any unethical work submitted for publication.

The major aim of this research is to study the auditor's Independence from Iranian Certified Accountants' Point of view. The result of this study indicate, That factors such as, audit commitlee, client's Size, the Size and experience of audit firms, increase anditor's Independence. Other factor, namely Competition between anditing firms decreases auditor's Independence.