2-distance Zero Forcing Sets in Graphs (European Journal of Pure and Applied Mathematics, 2024)
In this paper, we introduce new concept in graph theory called 2-distance zero forcing. We give some properties of this new parameter and investigate its connections with other parameters such as zero forcing and hop domination. We show that 2-distance zero forcing and hop domination (respectively, zero forcing parameter) are incomparable. Moreover, we characterize 2-distance zero forcing sets in some special graphs, and finally derive the exact values or bounds of the parameter using these results.
Keywords: Zero forcing set; 2-distance zero forcing set; 2-distance zero forcing number