In this study, we introduce a concept of connected total dominating neighborhood polynomial of a graph and establish relationships between the algebraic properties of this polynomial and the graph-theoretic properties of the neighborhood system of a connected total dominating set of a graph. Moreover, certain results on the connected total dominating neighborhood polynomials of some special graphs such as complete graphs, complete bipartite graphs, and complete q-partite graphs have been obtained.

dominating set, connected total dominating set, neighborhood system, connected total dominating neighborhood polynomial.

Received: January 20, 2023; Accepted: March 30, 2023; Published: May 23, 2023

How to cite this article: Rosalio G. Artes Jr., Rashidin H. Moh. Jiripa and Jeffrey Imer C. Salim, Connected total dominating neighborhood polynomial of graphs, Advances and Applications in Discrete Mathematics 39(2) (2023), 145-154. http://dx.doi.org/10.17654/0974165823042

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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