Domination Edge Integrity of Corona Products of C_n with P_m, C_m, K_(1,m)
Elgin Kılıç, Ayşe BEŞİRİK · Sinop Üniversitesi Fen Bilimleri Dergisi · 2021
Vulnerability is the most important concept in analysis of communication networks to disruption. Any network can be modelled by graphs so measures defined on graphs gives an idea in design. Integrity is one of the well-known vulnerability measures interested in remaining structure of a graph after any failure. Domination is also an another popular concept in network design. Nowadays new vulnerability measures take a great role in any failure not only on nodes also on links which have special properties. A new measure domination edge integrity of a connected and undirected graph was defined such as 𝐷𝐼′(𝐺)=𝑚𝑖𝑛{ |𝑆|+𝑚(𝐺−𝑆):𝑆 ⊆ 𝐸(𝐺)} where 𝑚(𝐺−𝑆) is the order of a maximum component of 𝐺−𝑆 and 𝑆 is an edge dominating set. In this paper some results concerning this parameter on corona products of graph structures 𝐶𝑛⊙𝐶𝑚, 𝐶𝑛⊙𝑃𝑚, 𝐶𝑛⊙𝐾1,𝑚 are presented.