Clique Irreducibility of Some Iterative Classes of Graphs

In this paper, two notions, the clique irreducibility and clique vertex irreducibility are discussed. A graph G is clique irreducible if every clique in G of size at least two, has an edge which does not lie in any other clique of G and it is clique vertex irreducible if every clique in G has a vertex which does not lie in any other clique of G. It is proved that L(G) is clique irreducible if and only if every triangle in G has a vertex of degree two. The conditions for the iterations of line graph, the Gallai graphs, the anti-Gallai graphs and its iterations to be clique irreducible and clique vertex irreducible are also obtained.

A Study of Closure and Fuzzy Closure Spaces with Reference to H-Closedness and Convexity

Department of Mathematics, Cochin University of Science and Technology.

Jerim-320: A New 320-Bit Hash Function Compared To Hash Functions With Parallel Branches

This paper describes JERIM-320, a new 320-bit hash function used for ensuring message integrity and details a comparison with popular hash functions of similar design. JERIM-320 and FORK -256 operate on four parallel lines of message processing while RIPEMD-320 operates on two parallel lines. Popular hash functions like MD5 and SHA-1 use serial successive iteration for designing compression functions and hence are less secure. The parallel branches help JERIM-320 to achieve higher level of security using multiple iterations and processing on the message blocks. The focus of this work is to prove the ability of JERIM 320 in ensuring the integrity of messages to a higher degree to suit the fast growing internet applications