scholarly journals The isoperimetric and Kazhdan constants associated to a Paley graph

2016 ◽  
Vol 9 (2) ◽  
pp. 293-306
Author(s):  
Kevin Cramer ◽  
Mike Krebs ◽  
Nicole Shabazi ◽  
Anthony Shaheen ◽  
Edward Voskanian
Keyword(s):  
Paley Graph

scholarly journals A New Symmetric Key Cryptographic Algorithm using Paley Graphs and ASCII Values

2021 ◽  
Vol 297 ◽  
pp. 01046
Author(s):  
Zhour Oumazouz ◽  
Driss Karim
Keyword(s):  
Brute Force ◽  
Strong Regularity ◽  
Quadratic Residues ◽  
Cryptographic Algorithm ◽  
Paley Graph ◽  
Encryption And Decryption ◽  
Symmetric Key ◽  
Brute Force Attack ◽  
The Moment ◽  
Paley Graphs

The main objective of the study conducted in this article is to introduce a new algorithm of encryption and decryption of a sensitive message after transforming it into a binary message. Our proposed encryption algorithm is based on the study of a particular graph constructed algebraically from the quadratic residues. We have exploited the Paley graph to introduce an abstract way of encryption of such message bit according to the other message bits by the intermidiate study of the neighborhood of a graph vertex. The strong regularity of the Paley graphs and the unknown behavior of the quadratic residues will play a very important role in the cryptanalysis part which allows to say that the brute force attack remains for the moment the only way to obtain the set of possible messages.

scholarly journals Lower bounds forr2(K1+G)andr3(K1+G)from Paley graph and generalization

2014 ◽  
Vol 40 ◽  
pp. 65-72
Author(s):  
Qizhong Lin ◽  
Yusheng Li ◽  
Jian Shen
Keyword(s):  
Lower Bounds ◽  
Paley Graph

Pseudo-telepathy games using graph states

2013 ◽  
Vol 13 (9&10) ◽  
pp. 833-845
Author(s):  
Anurag Anshu ◽  
Mehdi Mhalla
Keyword(s):  
Probability Distribution ◽  
Quantum Probability ◽  
Graph State ◽  
Graph States ◽  
Paley Graph

We define a family of pseudo-telepathy games using graph states that extends the Mermin games. This family also contains a game used to define a quantum probability distribution that cannot be simulated by any number of nonlocal boxes. We extend this result, proving that the probability distribution obtained by the Paley graph state on 13 vertices (each vertex corresponds to a player) cannot be simulated by any number of 4-partite nonlocal boxes and that the Paley graph states on $k^{2}2^{2k-2}$ vertices provide a probability distribution that cannot be simulated by $k$-partite nonlocal boxes, for any $k$.

scholarly journals Cliques and colorings in generalized Paley graphs and an approach to synchronization

2015 ◽  
Vol 14 (06) ◽  
pp. 1550088 ◽  
Author(s):  
Csaba Schneider ◽  
Ana C. Silva
Keyword(s):  
Finite Field ◽  
Directed Graph ◽  
Undirected Graph ◽  
Multiplicative Group ◽  
Permutation Groups ◽  
Chromatic Numbers ◽  
Paley Graph ◽  
Paley Graphs

Given a finite field, one can form a directed graph using the field elements as vertices and connecting two vertices if their difference lies in a fixed subgroup of the multiplicative group. If -1 is contained in this fixed subgroup, then we obtain an undirected graph that is referred to as a generalized Paley graph. In this paper, we study generalized Paley graphs whose clique and chromatic numbers coincide and link this theory to the study of the synchronization property in 1-dimensional primitive affine permutation groups.

A Random Model for the Paley Graph

2016 ◽  
Author(s):  
Rudi Mrazović
Keyword(s):  
Random Model ◽  
Paley Graph

The Paley graph conjecture and Diophantine m-tuples

2020 ◽  
Vol 170 ◽  
pp. 105155
Author(s):  
Ahmet M. Güloğlu ◽  
M. Ram Murty
Keyword(s):  
Paley Graph

scholarly journals Minimum Total Dominating Energy of Some Special Classes of Graphs

2020 ◽  
Vol 8 (4S5) ◽  
pp. 221-226
Keyword(s):  
Undirected Graph ◽  
Dominating Set ◽  
Domination Number ◽  
Total Domination ◽  
Total Domination Number ◽  
Minimum Cardinality ◽  
Total Dominating Set ◽  
Paley Graph ◽  
Eigen Values ◽  
Vertex Set

Let 𝑮 = (𝑽,𝑬) be a simple, finite, connected and undirected graph with vertex set V(G) and edge set E(G). Let 𝑺 ⊆ 𝑽(𝑮). A set S of vertices of G is a dominating set if every vertex in 𝑽 𝑮 − 𝑺 is adjacent to at least one vertex in S. A set S of vertices in a graph 𝑮(𝑽,𝑬) is called a total dominating set if every vertex 𝒗 ∈ 𝑽 is adjacent to an element of S. The minimum cardinality of a total dominating set of G is called the total domination number of G which is denoted by 𝜸𝒕 (𝑮). The energy of the graph is defined as the sum of the absolute values of the eigen values of the adjacency matrix. In this paper, we computed minimum total dominating energy of some special graphs such as Paley graph, Shrikhande graph, Clebsch graph, Chvatal graph, Moser graph and Octahedron graph.

scholarly journals Uniform Mixing and Association Schemes

10.37236/4745 ◽  
2017 ◽  
Vol 24 (3) ◽  
Author(s):  
Chris Godsil ◽  
Natalie Mullin ◽  
Aidan Roy
Keyword(s):  
Continuous Time ◽  
Hadamard Matrices ◽  
Quantum Walks ◽  
Association Schemes ◽  
Strongly Regular Graphs ◽  
Regular Graphs ◽  
Paley Graph ◽  
Time Quantum ◽  
Strongly Regular ◽  
Distance Regular Graphs

We consider continuous-time quantum walks on distance-regular graphs. Using results about the existence of complex Hadamard matrices in association schemes, we determine which of these graphs have quantum walks that admit uniform mixing.First we apply a result due to Chan to show that the only strongly regular graphs that admit instantaneous uniform mixing are the Paley graph of order nine and certain graphs corresponding to regular symmetric Hadamard matrices with constant diagonal. Next we prove that if uniform mixing occurs on a bipartite graph $X$ with $n$ vertices, then $n$ is divisible by four. We also prove that if $X$ is bipartite and regular, then $n$ is the sum of two integer squares. Our work on bipartite graphs implies that uniform mixing does not occur on $C_{2m}$ for $m \geq 3$. Using a result of Haagerup, we show that uniform mixing does not occur on $C_p$ for any prime $p$ such that $p \geq 5$. In contrast to this result, we see that $\epsilon$-uniform mixing occurs on $C_p$ for all primes $p$.

Maximal cliques in the Paley graph of square order

1996 ◽  
Vol 56 (1) ◽  
pp. 33-38 ◽  
Author(s):  
R.D. Baker ◽  
G.L. Ebert ◽  
J. Hemmeter ◽  
A. Woldar
Keyword(s):  
Paley Graph
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