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Alqesmah, Akram; Alwardi, Anwar; Rangarajan, R.

An atlas of injective domination polynomials of graphs of order at most six. (English) Zbl 1431.05085

Palest. J. Math. 9, No. 1, 48-61 (2020).
Summary: The injective domination polynomial of a graph \(G\) of order \(p\) is defined as \[D_{\mathrm{in}}(G, x) =\sum^p_{j= \gamma_{\mathrm{in}}(G)}d_{\mathrm{in}}(G, j)x^j, \] where \(\gamma_{\mathrm{in}}(G)\) is the injective domination number of \(G\) and \(d_{\mathrm{in}}(G,j)\) is the number of injective dominating sets of \(G\) of size \(j\). We call the roots of an injective domination polynomial of a graph the injective domination roots of that graph. In this article, we compute the injective domination polynomial of all graphs of order less than or equal six and their roots and present them in tables.

MSC:

05C31 Graph polynomials
05C69 Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.)
05C76 Graph operations (line graphs, products, etc.)

Keywords:

injective domination; injective domination polynomial
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\textit{A. Alqesmah} et al., Palest. J. Math. 9, No. 1, 48--61 (2020; Zbl 1431.05085)
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References:

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[2] Akram Alqesmah, Anwar Alwardi and R. Rangarajan, Edge injective domination of graphs, Gulf journal of Mathematics, 5 (2) (2017) 46-55. · Zbl 1370.05158
[3] Akram Alqesmah, Anwar Alwardi and R. Rangarajan, On the injective domination polynomial of graphs, Palestine journal of Mathematics, 7 (1) (2018) 234-242. · Zbl 1375.05141
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