In this paper, we introduced the concept of induced cycle polynomials of graphs. We established some algebraic properties of these polynomials with respect to graph-theoretic properties of graphs. For a given polynomial in the indeterminate x with coefficients in  we have shown that there exist infinitely many graphs with an induced cycle polynomial equal to the given polynomial. Moreover, we obtain induced cycle polynomials of some special graphs, such as cycles, fans, wheels, complete graphs, complete bipartite graphs, and complete q-partite graphs.

induced cycle, induced cycle polynomial, graph reconstruction.

Received: February 9, 2023; Accepted: March 4, 2023; Published: March 22, 2023

How to cite this article: Radana E. Madalim, Rolito G. Eballe, Abdurahman H. Arajaini and Rosalio G. Artes, Jr., Induced cycle polynomial of a graph, Advances and Applications in Discrete Mathematics 38(1) (2023), 83-94. http://dx.doi.org/10.17654/0974165823020

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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