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

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.) |

### References:

[1] | Akram Alqesmah, Anwar Alwardi and R. Rangarajan, Connected injective domination of graphs, Bulletin of the International Mathematical Virtual Institute, 7 (2017) 73-83. · Zbl 1412.05143 |

[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 |

[4] | S. Alikhani, Dominating sets and domination polynomials of graphs: Domination polynomial: A new graph polynomial, LAMBERT Academic Publishing, ISBN: 9783847344827 (2012). |

[5] | Anwar Alwardi, Akram Alqesmah and R. Rangarajan, Independent injective domination of graphs, Int. J. Adv. Appl. Math. and Mech. 3 (4) (2016) 142-151. · Zbl 1367.05152 |

[6] | Anwar Alwardi, R. Rangarajan and Akram Alqesmah, On the Injective domination of graphs, Palestine journal of Mathematics, 7 (1) (2018) 202-210. · Zbl 1375.05189 |

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