Given n vertices and m edges, m ≥ 1, and for every vertex is given a label, there are lots of graphs that can be obtained. The graphs obtained may be simple or not simple, connected or disconnected. A graph G(V,E) is called simple if G(V,E) not containing loops nor paralel edges. An edge which has the same end vertex is called a loop, and paralel edges are two or more edges which connect the same set of vertices. Let N(G7,m,t) as the number of connected vertex labeled graphs of order seven with m vertices and t (t is the number edges that connect different pair of vertices). The result shows that N(G7,m,t) = ct C (m−1) t−1, with c6=6727, c7=30160 , c8=30765, c9=21000, c10=28364, c11=26880, c12=26460, c13=20790, c14=10290, c15= 8022, c16=2940, c17=4417, c18=2835, c19=210, c20= 21, c21=1.

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Determining The Number of Connected Vertex Labeled Graphs of Order Seven without Loops by Observing The Patterns of Formula for Lower Order Graphs with Similar Property

Encryption and decryption are the two processes in cryptography to conceal and convey important information to an authorized person without third-party interruption in a network. Cryptography is a branch of computer science in which the system has to be updated every second. It mainly depends on mathematical concepts like number theory and algebra. Recently, graph theory concepts are employed in cryptography to make it stronger. The usage of complex graphs in cryptosystems makes it difficult to hack. In this paper, we proposed a cryptosystem using the Turan graph which has a complex graph structure. The advantage of using a Turan graph is that it is a unique multipartite complete graph with more edges than other multipartite complete graphs. This adds robustness to the cryptosystem. The novelty of this paper is the decomposition of the Turan graph into paths and stars and applying edge labeling to them to encrypt and decrypt a sentence of <math xmlns="http://www.w3.org/1998/Math/MathML" id="M1"> <mi>k</mi> </math> words. The algorithms for encryption and decryption are also proposed in this paper. 

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Block Encryption and Decryption of a Sentence Using Decomposition of the Turan Graph

Encryption and decryption of signed graph matrices through RSA algorithm

Presented cancelable face recognition system using graph theory

In today’s technological world, confidentiality is an important issue to deal with, and it is carried out through different proficiencies. Cryptography is a scientific technique of securing a communication from unauthenticated approach. There exist many encryption algorithms in cryptography for data security. The need of new nonstandard encryption algorithms has been raised to prevent the communication from traditional attacks. This paper proposes some new encryption algorithms for secure transmission of messages using some special corona graphs and bipartite graph along with some algebraic properties. These proposed encryption schemes will lead to more secure communication of secret messages.

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Rabiha Qazi

Papers

Some Graph-Based Encryption Schemes