The doctrine that the Content of the conclusion of a deductively valid argument is included in the Content of its premises, taken jointly, is a familiar one. It has important consequences for the question of what value valid arguments possess, since it indicates the poverty of three traditional answers: that arguments may and should be used as instruments of persuasion, that they may and should be used as instruments of justification; and that they may and should be used to advance knowledge. The truth is, however, that in each of these cases the argument has only a managerial role and, if there is any work done, it is the premises that do it. It will be maintained that this point has little force against the critical rationalist answer, which I shall defend, that the principal purpose of deductive reasoning from an assemblage of premises is the exploration of their Content, facilitating their criticism and rejection. That said, the main aim of the present paper is not to promote critical rationalism but to consider some published objections to the doctrine that a statement asserts every statement that is validly deducible from it. The alleged counterexamples to be considered fall roughly into two groups: statements that emerge with time from a rich mathematical or empirical theory, but were originally unformulated and are deducible from the theory only in a non-trivial way (Frederick 2011, 2014; Williamson 2012); and statements, notably disjunctions, that are easily formulated and are deducible from a theory in a trivial way (Schurz & Weingartner 1987; Mura 1990, 2008; Gemes 1994; Yablo 2014). Each of these counterexamples will be evaluated and dismissed.

Researchers have always been interested in Graph nodes clustering based on Content or structure. But less attention has been paid to clustering based on both structure and Content. But a Content-structural clustering is needed in information networks like social networks. In this paper, the ICS-Cluster algorithm is proposed which takes into consideration both the structure and Content aspects of the nodes. The purpose of this approach is to gain a coherent internal structure (structural aspect) and homogeneous attribute values (Content aspect) in the Graph. In this approach firstly the Graph is converted into a Content-structural Graph which edges' weight show similarity between the connected nodes. Incremental clustering is done based on edges’ weight in this process the edges with the most weight is considered as clusters then the weight of connected edge to the cluster is aggregated and they’ ll be one edge, the process is repeated until the algorithm reaches the number of clusters that indicated by the user. ICS-Cluster algorithm number of cluster is indicated by the user. Comparing ICS-Cluster with other Content structural algorithm based on six criteria for measuring cluster quality shows that ICS-Cluster has good performance. These criteria contain structural criteria (Modularity, Error Link, and Density), Content criterion (Average Similarity), Content-structural criterion (CS-Measure) and the run time.

Entities in social networks, in addition to having the relationship with each other, also have Content. This type of networks can be modeled by the enriched Graph, in which nodes could have text too. Graph clustering is one of the important attempts toward analyzing social networks. Despite these two facts, most of the existing Graph clustering methods independently focused on one of the Content or structural aspects. Content-Structural Graph clustering algorithms simultaneously consider both the structure and the Content of the Graph. The main aim of this paper is to achieve well connected (structured) clusters while their nodes benefit from homogeneous attribute values (Content). The proposed algorithm in this paper so-called RSL-Cluster performs the clustering by hierarchically removing the edge between nodes which has a weight lower that the average similarity of nodes. This stage continues until reaching the user’ s desired number of clusters. Comparing the proposed algorithm with three well-known Content-structural clustering algorithms represents the proper functioning of the proposed method. The used measures to evaluate our method include structural, Content and the Content-structural measures.

Telegram is a cloud-based instant messenger with more than 500 million monthly active users. This messenger is very popular among Iranians, as more than 50 million Telegram users are Iranians. Telegram is used as a social network in Iran because it offers features beyond a simple messenger, but does not offer all the features of social networks, including user recommendation. In this paper, investigating a real dataset crawled from Telegram, we have provided a hybrid method using the user membership Graph and group characteristics to recommend the user in Telegram. The membership Graph connects users based on membership in the same groups. Also, the characteristics for each group are indicated by the name and description of that group in Telegram. We created a bag of words for each group using natural language processing methods, then combined the bag of words for each group with the results of the membership Graph processing. Finally, users are recommended based on the list of groups obtained by the combination. The data used in this paper include more than 900, 000 groups and 120 million users. Evaluation of the proposed method separately on two categories of Telegram specialized groups shows the model integration and error reduction for the first category to 0. 009 and the second category to 0. 016 in RMSE.

Today, with the spread of social networks, the opposition's efforts to chill out people from government (known as “ soft war” ) are increased. Therefore, dealing with this type of networks is important for military and security organizations. Graph clustering is one of the first attempts toward analyzing social networks which can appropriately be modeled by a Content Graph. In contrast, most of the existing Graph clustering methods independently focused on one of the Content or structural aspects of a Graph. The aim of this paper (implemented as CS-Cluster algorithm) is to achieve well connected clusters while their nodes benefits from homogeneous attribute values (Content). In the second step of our research, after an intensive search, no measure has found which could simultaneously consider Content and structural features of clustering algorithms. So to be able to appropriately evaluate our algorithm, a new Content-structural measure (so-called “ CS-Measure” ) is proposed. Our experimentation shows that the proposed clustering algorithm outperforms two other well-known Content-structural clustering algorithms, using the new Content-structural, average similarity, and Error link measure as well as the previous Content and structural measures, And it also performed relatively well in density measure.

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.

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.

Let R be a commutative ring and M be an R-module. The M-intersection Graph of ideals of R, denoted by GM(R) is a Graph with the vertex set I(R) ∗, , and two distinct vertices I and J are adjacent if and only if IM ∩,JM ̸, = 0. In this paper, we study GR/J (R/I), where I and J are ideals of R and I ⊆,J. We characterize all ideals I and J for which GR/J (R/I) is planar, outerplanar or ring Graph.

‎Graph coloring is the assignment of one color to each vertex of a Graph so that two adjacent vertices are not of the same color‎. ‎The Graph coloring problem (GCP) is a matter of combinatorial optimization‎, ‎and the goal of GCP is determining the chromatic number $\chi(G)$‎. ‎Since GCP is an NP-hard problem‎, ‎then in this paper‎, ‎we propose a new approximated algorithm for finding the coloring number (it is an approximation of chromatic number) by using a Graph adjacency matrix to colorize or separate a Graph‎. ‎To prove the correctness of the proposed algorithm‎, ‎we implement it in MATLAB software‎, ‎and for analysis in terms of solution and execution time‎, ‎we compare our algorithm with some of the best existing algorithms that are already implemented in MATLAB software‎, ‎and we present the results in tables of various Graphs‎. ‎Several available algorithms used the largest degree selection strategy‎, ‎while our proposed algorithm uses the Graph adjacency matrix to select the vertex that has the smallest degree for coloring‎. ‎We provide some examples to compare the performance of our algorithm to other available methods‎. ‎We make use of the Dolan-Mor\'e performance profiles to assess the performance of the numerical algorithms‎, ‎and demonstrate the efficiency of our proposed approach in comparison with some existing methods‎.

Let $G=(V,E)$ be a Graph of order $n$ and size $m.$ The Graph $Sp(G)$ obtained from $G$ by adding a new vertex $v'$ for every vertex $v\in V$ and joining $v'$ to all neighbors of $v$ in $G$ is called the splitting Graph of $G.$ In this paper, we determine the domination number, the total domination number, connected domination number, paired domination number and independent domination number for the splitting Graph $Sp(G).$