hamid reza maimani

For a graph $G$, a set $L$ of vertices is called a total liar's domination if $|N_G(u)cap L|geq 2$ for any $uin V(G)$ and $|(N_G(u)cup N_G(v))cap L|geq 3$ for any distinct vertices $u,vin V(G)$. The total liar’s domination number is the cardinality of a minimum total liar’sdominating set of $G$ and is denoted by $gamma_{TLR}(G)$. In this paper we study the total liar's domination numbers of join and products of graphs.

Linear diffusion layer is an important part of lightweight block ciphers and hash functions. This paper presents an efficient class of lightweight 4x4 MDS matrices such that the implementation cost of them and their corresponding inverses are equal. The main target of the paper is hardware oriented cryptographic primitives and the implementation cost is measured in terms of the required number of XORs. Firstly, we mathematically characterize the MDS property of a class of matrices (derived from the product of binary matrices and companion matrices of $\sigma$-LFSRs aka recursive diffusion layers) whose implementation cost is $10m+4$ XORs for 4 <= m <= 8, where $m$ is the bit length of inputs. Then, based on the mathematical investigation, we further extend the search space and propose new families of 4x 4 MDS matrices with 8m+4 and 8m+3 XOR implementation cost. The lightest MDS matrices by our new approach have the same implementation cost as the lightest existent matrix.

A set $D$ of vertices of graph $G$ is called $double$ $dominating$ $set$ if for any vertex $v$, $|N[v]cap D|geq 2$. The minimum cardinality of $double$ $domination$ of $G$ is denoted by $gamma_d(G)$. The minimum number of edges $E'$ such that $gamma_d(Gsetminus E)>gamma_d(G)$ is called the double bondage number of $G$ and is denoted by $b_d(G)$. This paper determines that $b_d(Gvee H)$ and exact values of $b(P_ntimes P_2)$, and generalized corona product of graphs.

One of the important parameters of the secret sharing scheme is information rate, which defines the size of distributed information among the shareholders corresponds to size of their secret key. Generally, for any given access structure, it is not possible that one can find the information rate of secret sharing schemes. In this paper, an upper bound of information rate is presented with using independent sequence method, then, we study secret sharing schemes whose access structure has five minimal qualified subsets such that the ideal secret sharing schemes case some of the characterized and for the non-ideal case we provide bounds on the optimal information rate.

The purpose of this paper is to study the information ratio of perfect secret sharing of product of some special families of graphs. We seek to prove that the information ratio of prism graphs $Y_{n}$ are equal to $frac{7}{4}$ for any $ngeq 5$, and we will gave a partial answer to a question of Csirmaz cite{CL}. We will also study the information ratio of two other families $C_{m}times C_{n}$ and $P_{m}times C_{n}$ and obtain the exact value of information ratio of these graphs.

Let R be a commutative ring with $Z(R)$ its set of zero-divisors. In this paper, we study the total graph of $R$, denoted by $T(Gamma(R))$. It is the (undirected) graph with all elements of R as vertices, and for distinct $x, yin R$, the vertices $x$ and $y$ are adjacent if and only if $x + yinZ(R)$. We study the chromatic number and edge connectivity of this graph.