eng Science and Education Publishing American Journal of Numerical Analysis 2372-2126 2018-01-09 5 1 11 15 10.12691/ajna-5-1-2 AJNA2017512 article H. S. Ramane 1 S.C. Shiralashetti 1 R. A. Mundewadi rkmundewadi@gmail.com 2 R. B. Jummannaver 2 Department of Mathematics, Karnatak University, Dharwad, India P.A. College of Engineering, Mangalore, India The main purpose of this paper is to develop the graph theoretic polynomial to solve numerical problems. We present a new method for the solution of Fredholm integral equations using Hosoya polynomials obtained from one of the standard class of graphs called as path. Proposed algorithm expands the desired solution in terms of a set of continuous polynomials over a closed interval [0,1]. However, accuracy and efficiency are dependent on the size of the set of Hosoya polynomials and compared with the existing method. http://pubs.sciepub.com/ajna/5/1/2/ajna-5-1-2.pdf Fredholm integral equations Hosoya polynomial path