Abstract: 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.
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Keywords and phrases: star, induced star, star polynomial.
Received: January 10, 2023; Revised: January 21, 2023: Accepted: January 25, 2023; Published: January 28, 2023
How to cite this article: Rosalio G. Artes, Jr., Nurijam Hanna R. Mohammad, Amy A. Laja and Nur-Hariza M. Hassan, From graphs to polynomial rings: Star polynomial representation of graphs, Advances and Applications in Discrete Mathematics 37 (2023), 67-76. http://dx.doi.org/10.17654/0974165823012
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References:
[1] R. Artes and L. Laja, Zeros of convex subgraph polynomials, Appl. Math. Sci. 8(59) (2014), 2917-2923. [2] R. Artes, M. Langamin and A. Calib-og, Clique common neighborhood polynomial of graphs, Advances and Applications in Discrete Mathematics 35 (2022), 77-85. [3] J. Ellis-Monaghan and J. Merino, Graph Polynomials and their Applications II: Interrelations and Interpretations, Birkhauser, Boston, 2011. [4] G. Entero and A. Pedrano, On connected total domination polynomial of some lexicographical product of graphs, Advances and Applications in Discrete Mathematics 27(1) (2021), 147-155. [5] I. Gutman, Graphs and Graph Polynomials of Interest in Chemistry, G. Tinhofer and G. Schmidt, eds., Lecture Notes in Computer Science, Springer-Verlag, Berlin, 2005, pp. 177-187. [6] C. Hoede and X. Li, Clique polynomials and independent set polynomials of graphs, Discrete Mathematics 125 (1994), 219-228.
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