Bounds of Location-2-Domination Number for Products of Graphs

Abstract

In this paper Location-2-Domination set and their properties are being studied. A subset V S ⊆ is Location-2-Dominating set of G if S is 2-Dominating set of G and for any two vertices P W × , n m C S × P n ⋈P m , C n ⋈P m , C n ⋈C m have been found.

Graphs Defined on Rings: A Review

“…Euler totient Cayley graphs were introduced in [114], in which the basic properties of the graphs were studied, and the values of n for which the graph was a standard graph class were classified and characterised. Using this study, various types of domination were discussed and the corresponding domination parameters were determined in [115][116][117][118][119][120][121][122]. The results on the domination number of the Euler totient Cayley graph proven in [120] were the motivation to investigate the tightness of the bounds of the domination number in terms of the Jacobsthal function, as given in [107,108].…”

The Minimum Total Edge Dominating Energy of a Graph

“…Its eigenvalues are real number the energy ‫)ܩ(ܧ‬ of graph is defined to the sum of absolute values of its eigenvalues of graph ‫ܩ‬ that is ‫)ܩ(ܧ‬ = ∑ |ߣ | ଵ . Motivated by the research articles, A survey on energy of a graph [8], energies like Distance energy [2], Minimum covering energy [1], Incidence energy [6], Lalpacian energy [5], Domination in graphs [7,9], and importance of domination number [3], we introduced the minimum total edge dominating energy is defined in this paper and same is obtained for some standard graphs.…”