Volume 68 | Issue 3 | Year 2022 | Article Id. IJMTT-V68I3P510 | DOI : https://doi.org/10.14445/22315373/IJMTT-V68I3P510

A shortest path between two vertices in a graph G is a geodesic in G A graph polynomial is a graph invariant. There are many graph polynomials can be found in the literature including, the characteristic polynomial, the chromatic polynomial and so on. This paper aims at the study of two new graph polynomials associated with the geodesics in a graph introduced by R. Rajendra and P.S.K. Reddy, namely, the geodesic polynomial of a graph and the geodesic polynomial at a vertex in a graph. We obtain some results involving geodesic polynomials of graphs and geodesic polynomials at the vertices

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Swamy, N. D. Soner, B. M. Chandrashekara, "The Geodesic Polynomials in a Graph," *International Journal of Mathematics Trends and Technology (IJMTT)*, vol. 68, no. 3, pp. 52-58, 2022. *Crossref*, https://doi.org/10.14445/22315373/IJMTT-V68I3P510