Chemical Formula Encryption - using Hamiltonian Circuits and Graph Valued Functions

The ever expanding nature of graph theory has made it a convenient tool for a wide range of practical applications. This study prescribes an algorithmic approach of cryptographic decoding of chemical formula using Jump graphs and Line graphs. Hamiltonian graphs are used as the key for encryption and decryption.

Some new theoretical work on Half Butterfly Method for Hamiltonian circuit in complete graph

A new method to construct the distinct Hamiltonian circuits in complete graphs is called Half Butterfly Method. The Half Butterfly method used the concept of isomorphism in developing the distinct Hamiltonian circuits. Thus some theoretical works are presented throughout developing this method.

MEMRISTOR HAMILTONIAN CIRCUITS

We prove analytically that 2-element memristive circuits consisting of a passive linear inductor in parallel with a passive memristor, or an active memristive device, can be described explicitly by a Hamiltonian equation, whose solutions can be periodic or damped, and can be represented analytically by the constants of the motion along the circuit Hamiltonian. Generalizations to 3-element and 2N-element memristive Hamiltonian circuits are also presented where complex bifurcation phenomena including chaos, abound.