The Minimum Dominating Energy of a Graph

Abstract

Recently Professor Chandrashekar Adiga et al [3] defined the minimum covering energy, E C (G) of a graph which depends on its particular minimum cover C. Motivated by this, we introduced minimum dominating energy of a graph E D (G) and computed minimum dominating energies of a star graph, complete graph, crown graph and cocktail graphs. Upper and lower bounds for E D (G) are established.

Energy of Bipolar Fuzzy Graphs

“…Akram et al [3] discussed Laplacian and singless Laplacian energy of bipolar fuzzy graphs and bipolar fuzzy digraphs. For further terminologies and studies on energy of fuzzy graphs and their extensions, readers are referred to [1,2,6,[10][11][12][17][18][19].…”

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.…”

Minimum covering distance energy of a graph

“…Detailed studies on distance energy can be found in [5,9,15,16,21]. Further studies on covering energy,maximum degree energy, dominating energies can be found in [1,2,19,20]and the references cited there in.…”