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FROM GRAPHS TO POLYNOMIAL RINGS: STAR POLYNOMIAL REPRESENTATION OF GRAPHS
Keywords:
star, induced star, star polynomial.DOI:
https://doi.org/10.17654/0974165823012Abstract
Let $G$ be a simple connected graph. An $i$-subset of $V(G)$ is a subset of $V(G)$ of cardinality $i$. An induced $i$-star of $G$ is a star in $G$ induced by an $i$-subset of $V(G)$. The star polynomial representation of $G$ is the generating function of the sequence of the number of induced $i$-stars in $G$. In this paper, we establish the star polynomials of some special graphs such as the star graph, spider graph, complete bipartite graph, and the complete $q$-partite graph.
Received: January 10, 2023;
Revised: January 21, 2023:
Accepted: January 25, 2023;
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