Gutman and Degree Monophonic Index of Graphs
V. Kaladevi1, G. Kavitha2
1V. Kaladevi, Department of Mathematics, Nirmala College, Affiliated to University of Madras, Trichirapalli, Chennai, India
2G. Kavitha, Department of Mathematics, Hindustan Institute of Technology & Science, Chennai, India.
Manuscript received on 30 June 2019 | Revised Manuscript received on 05 July 2019 | Manuscript published on 30 July 2019 | PP: 1982-1989 | Volume-8 Issue-9, July 2019 | Retrieval Number: I8911078919/19©BEIESP | DOI: 10.35940/ijitee.I8911.078919
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Abstract: A graph with p points and q edges is denoted by G(p,q). An edge joining two non-adjacent points of a path P is called a chord of a path P. A path P is called monophonic if it is a chordless path. For any two points u and v in a connected graph G, the monophonic distance dm (u, v) m from u to v is defined as the length of a longest u-v monophonic path in G. The Gutman monophonic index of a graph G is denoted by Gut MP (G) and defined by GutMP(G)=∑d(u)d(ν) and degree monophonic index of G is denoted by DMP(G) and defined by DMP(G) d(u) d(v)d (u,v)   m . The methodology executed in this research paper is to determine the monophonic distance matrix of graphs under consideration. The entries of monophonic distance matrix are calculated by counting the number of edges in the u-v monophonic path. In this paper for some standard graphs, GutMP(G) and DMP(G) are studied which can be applied to derive quantitative structure- property or structure- activity relationships (QSPR / QSAR). Index Terms: Degree Monophonic Index, Gutman Monophonic Index, Monophonic Index, Monophonic Path.
Scope of the Article: Bio – Science and Bio – Technology