International Journal of Engineering, Science and Mathematics Vol. 6 Issue 7, November 2017, ISSN: 2320-0294 Impact Factor: 6.238 Journal Homepage: http://www.ijesm.co.in, Email: ijesmj@gmail.com Double-Blind Peer Reviewed Refereed Open Access International Journal - Included in the International Serial Directories Indexed & Listed at: Ulrich's Periodicals Directory ©, U.S.A., Open J-Gage as well as in Cabell’s Directories of Publishing Opportunities, U.S.A 57 International Journal of Engineering, Science and Mathematics http://www.ijesm.co.in, Email: ijesmj@gmail.com GRAPHS OF NEUROPEPTIDES INVOLVED IN LEARNING AND MEMORY PROCESSES Suresh Singh G. 1 , Department of Mathematics, University of Kerala, Kariavattom, Thiruvananthapuram – 695581, Kerala, India, Akhil C. K. 2 Department of Mathematics, University of Kerala, Kariavattom, Thiruvananthapuram – 695581, Kerala, India, Abstract Graph theoretical analysis is an important area of research in biological networks. In this work we defined a new graph called Neuropeptide  ∗∗ − graph obtained from  ∗∗ − set of each protein/peptide graphs of fifteen neuropeptides which involved in the brain function – learning and memory processes. From the graph theoretical analysis we got some observations about the relation among the fifteen neuropeptides. The highest centrality measures of the neuropeptides Beta-endorphin, Galanin, Neuropeptide Y, Oxytocin and Substance P revealed the critical vertices of the graph and they also gave the prominent neuropeptides involved in the learning and memory processes. The neuropeptide  ∗∗ − graph showed that all the neuropeptides were connected because every pairs of neuropeptides were inter related by atleast one amino acid which recieved atleast one highest centrality measure and revealed the strength of the relation between neuropeptides with in the brain function – learning and memory processes. This work may help in the study of the mechanisms involved in learning, memory processes and other brain functions and would aid in developing better solutions to treat diseases like Alzheimer’s. Its application may also help in the study of the evolution of neuropeptides involved in learning and memory processes and other brain functions in different species of animals. Keywords: Amino acid, neuroeptide, Pt-graph, Neuropeptide graph, Centrality measure. Copyright © 2017 International Journals of Multidisciplinary Research Academy. All rights reserved. Author correspondence: Akhil C. K., Department of Mathematics, University of Kerala, Kariavattom, Thiruvananthapuram – 695581, Kerala, India, 1. Introduction Proteins are polymers of amino acids, with each amino acid residue joined to its neighbour by a specific type of covalent bond [3]. Twenty different types of natural amino acids are commonly found in peptide/protein. The sequence of amino acids in a protein is characteristic of that protein and is called its primary structure [3]. Peptides/proteins are the compounds of amino acids in which a carboxyl group of one is united with an amino group of another. Neuropeptides are peptides formed and released by neurons. They are involved in a wide range of brain functions. The role of neuropeptides in cognitive functions including learning and memory processes has been studied earlier [6]. Moreover, neuropeptides may be of importance in neurogenerative and neuropsychiatric disorders associated with cognitive impairments. Cognition is the mental activities associated with thought, decision making, language and other higher mental processes like learning,