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CONVEX SUBGRAPH POLYNOMIALS OF DEGREE 3 OR 4, ROOTED AND CO-NORMAL PRODUCTS OF GRAPHS
Keywords:
convex set, convex subgraph polynomial.DOI:
https://doi.org/10.17654/0974165824002Abstract
A convex subgraph of a connected graph $G$ of order $n$ is a subgraph $\langle S\rangle$ induced by a convex subset $S$ of $V(G)$. The convex subgraph polynomial of $G$ is the polynomial
$$
C(G, x)=\sum_{i=0}^n c_i(G) x^i,
$$
where $c_i(G)$ is the number of convex subgraphs of $G$ of order $i$. This study enumerates all possible convex subgraph polynomials having degree 3 or 4 . This also characterizes a convex set in the rooted product $G \bullet H$ and the co-normal product $G * H$. The convex subgraph polynomials of these graph operations are also established.
Received: October 12, 2023
Revised: November 24, 2023
Accepted: December 5, 2023
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