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Let G be a group. The intersection graph of G, denoted by Γ(G), is the graph whose vertex set is the set of all nontrivial proper subgroups of G and two distinct vertices H and K are adjacent if and only if H ∩ K ≠= 1. In this paper, we show that the girth of Γ(G) is contained in the set {3,∞ }. We characterize all solvable groups whose intersection graphs are triangle-free. Moreover, we show that if G is finite and Γ (G) is triangle-free, then G is solvable. Also, we prove that if Γ (G) is a triangle-free graph, then it is a disjoint union of some stars. Among other results, we classify all abelian groups whose intersection graphs are complete. Finally, we study the intersection graphs of... 

Let R be a ring with identity and M be a unitary left R-module. The complement of the intersection graph of submodules of M, denoted by Γ(M), is defined to be a graph whose vertices are in one-to-one correspondence with all nontrivial submodules of M and two distinct vertices are adjacent if and only if the corresponding submodules of M have zero intersection. In this paper, we consider the complement of the intersection graph of submodules of a module. We prove that, if Γ(M) is connected and Δ(Γ(M)) < ∞, then M is semisimple, where Δ(Γ(M)) is the maximum degree of Γ(M). We show that, if Γ(M) is a forest, then each component of Γ(M) is a star graph. Moreover, it is proved that, if Γ(M) is a... 

Let R be a ring with identity and M be a unitary left R-module. The intersection graph of submodules of M, denoted by G(M), is defined to be a graph whose vertices are in one to one correspondence with all non-trivial submodules of M and two distinct vertices are adjacent if and only if the corresponding submodules of M have non-zero intersection. In this paper, we consider the intersection graph of submodules of a module. We determine the structure of modules whose clique numbers are finite. We show that if 1 < ω(G(M)) < ∞, then M is a direct sum of a finite module and a cyclic module, where ω(G(M)) denotes the clique number of G(M). We prove that if ω(G(M)) is not finite, then M contains... 

Let R be a ring with identity and M be a unitary left R-module. The intersection graph of an R-module M, denoted by G(M), is defined to be the undirected simple graph whose vertices are in one to one correspondence with all non-trivial submodules of M and two distinct vertices are adjacent if and only if the corresponding submodules of M have nonzero intersection. We investigate the interplay between the module-theoretic properties of M and the graph-theoretic properties of G(M). We characterize all modules for which the intersection graph of submodules is connected. Also the diameter and the girth of G(M) are determined. We study the clique number and the chromatic number of G(M). Among... 

Let be a ring and be the set of all non-trivial left ideals of. The intersection graph of ideals of, denoted by, is a graph with the vertex set and two distinct vertices and are adjacent if and only if. In this paper, we classify all rings (not necessarily commutative) whose domination number of the intersection graph of ideals is at least 2. Moreover, some results on the intersection graphs of ideals of matrix algebras over a finite field are given. For instance, we determine the domination number, the clique number and the independence number of. We prove that if is a positive integer and, then the domination number of is. Among other results, we show that if, where is a positive integer... 

Recently, there has been shown a great interest in the private set intersection (PSI) protocols which are widely used in social networks applications. In a PSI protocol two entities are able to find the intersection of their document set without inferring more information than the common data. In some PSI protocols the process of finding the intersections of the documents are delegated to a third entity like cloud which has high computational and storage resources and the clients can verify the accuracy of the received results. These protocols are known as the Verifiable Delegated Set Intersection (VDSI). In this paper, we proposed an efficient VDSI protocol by employing the El-Gamal... 

One of the frequent aspects of lawlessness at signalized intersections is red light violation (RLV). In addition to adverse effects on intersection safety, RLV can cause delay in the startup of the vehicles in the competing phase, defined as the green flow in this study. In this research, a video camera was used to collect the required data from intersections to investigate the adverse effect of RLV in the city of Esfahan, Iran. Then, by assigning a cellular network to the conflict points of the vehicles path in successive phases, the vehicles arrival times to these cells were measured and the imposed delays to the green flow were measured. The results of this study showed that the behavior... 

Analyzing motion patterns in traffic videos can be employed directly to generate high-level descriptions of their content. For traffic videos captured from intersections, usually, we can easily provide additional information about traffic phases. Such information can be obtained directly from the traffic lights or through traffic lights controllers. In this paper, we focus on incorporating additional information to analyze the traffic videos more efficiently. Using side information on traffic phases, the semantic of motion patterns from traffic intersection scenes can be learned more effectively. The learning is performed based on optical flow features extracted from training video clips,... 

A μ-way latin trade of volume s is a set of μ partial latin rectangles (of inconsequential size) containing exactly the same s filled cells, such that if cell (i, j) is filled, it contains a different entry in each of the μ partial latin rectangles, and such that row i in each of the μ partial latin rectangles contains, set-wise, the same symbols and column j, likewise. In this paper we show that all μ-way latin trades with sufficiently large volumes exist, and state some theorems on the non-existence of μ-way latin trades of certain volumes. We also find the set of possible volumes (that is, the volume spectrum) of μ-way latin trades for μ = 4 and 5. (The case μ = 2 was dealt with by Fu,... 

For a block design D, a series of block intersection graphs G i, or i-BIG(D), i = 0,..., k is defined in which the vertices are the blocks of D, with two vertices adjacent if and only if the corresponding blocks intersect in exactly i elements. A silver graph G is defined with respect to a maximum independent set of G, called an α-set. Let G be an r-regular graph and c be a proper (r + 1)-coloring of G. A vertex x in G is said to be rainbow with respect to c if every color appears in the closed neighborhood N[x] = N(x) ∪ {x}. Given an α-set I of G, a coloring c is said to be silver with respect to I if every x ∈ I is rainbow with respect to c. We say G is silver if it admits a silver... 

Let R be a ring with unity and I(R)* be the set of all nontrivial left ideals of R. The intersection graph of ideals of R, denoted by G(R), is a graph with the vertex set I(R)* and two distinct vertices I and J are adjacent if and only if I ∩ J ≠ 0. In this paper, we study some connections between the graph-theoretic properties of this graph and some algebraic properties of rings. We characterize all rings whose intersection graphs of ideals are not connected. Also we determine all rings whose clique number of the intersection graphs of ideals is finite. Among other results, it is shown that for a ring R, if the clique number of G(R) is finite, then the chromatic number is finite and if R is... 

Let Δ be a simplicial complex and χ be an s-coloring of Δ. Biermann and Van Tuyl have introduced the simplicial complex Δχ. As a corollary of Theorems 5 and 7 in their 2013 article, we obtain that the Stanley–Reisner ring of Δχ over a field is Cohen–Macaulay. In this note, we generalize this corollary by proving that the Stanley–Reisner ideal of Δχ over a field is set-theoretic complete intersection. This also generalizes a result of Macchia  

Flows generated by density differences are called gravity or density currents which are generic features of many environmental flows. These currents are classified as the conservative and non-conservative flows whether the buoyancy flux is conserved or changed respectively. In this paper, a low Reynolds k-ε turbulence model is used to simulate three dimensional density and turbidity currents. Also, a series of experiments were conducted in a straight channel to study the characteristics of the non-conservative density current. In experiments, Kaolin was used as the suspended material. Comparisons are made between conservative and non-conservative's height, concentration and velocity profiles... 

In recent years, determining the common information privately and efficiently between two mutually mistrusting parties have become an important issue in social networks. Many Private set intersection (PSI) protocols have been introduced to address this issue. By applying these protocols, two parties can compute the intersection between their sets without disclosing any information about components that are not in the intersection. Due to the broad range of computational resources that the cloud can provide for its users, determining the set intersection by cloud may decrease the computational cost of the users. The proposed protocol by Abadi et al. is one of the introduced protocols in this...