TRANSIT INDEX OF A GRAPH AND ITS CORRELATION WITH MON OF OCTANE ISOMERS
K. M. Reshmi and R. Pilakkat
Many topological indices are defined for Graphs. Some are distance based and some are degree based. Topological indices are widely used to analyse various networks, from large complex networks in communications to molecular graphs in chemical graph theory. In this paper we define new graph parameters called transit of a vertex and transit index of a graph. We compute them for Paths and Trees. It is found that among all trees on n vertices, the path $P_n$ has the maximum transit index. The bounds for transit index are determined for connected graphs. Finally, the correlation coefficient between transit index of molecular graphs of octane isomers and motor octane number is evaluated. The correlation coefficient obtained is strongly negative.
Keywords: Topological Index, Shortest path, Transit, Transit Index.