3 research outputs found
On Energy, Laplacian Energy and -fold Graphs
For a graph having adjacency spectrum (-spectrum) and Laplacian spectrum (-spectrum) , the energy is defined as and the Laplacian energy is defined as . In this paper, we give upper and lower bounds for the energy of and as a consequence we generalize a result of Stevanovic et al. [More on the relation between Energy and Laplacian energy of graphs, MATCH Commun. Math. Comput. Chem. {\bf 61} (2009) 395-401]. We also consider strong double graph and strong -fold graph to construct some new families of graphs for which E(G)> LE(G)
On Scores, Losing Scores and Total Scores in Hypertournaments
A -hypertournament is a complete -hypergraph with each -edge endowed with an orientation, that is, a linear arrangement of the vertices contained in the edge. In a -hypertournament, the score (losing score ) of a vertex is the number of arcs containing in which is not the last element (in which is the last element). The total score of is defined as . In this paper we obtain stronger inequalities for the quantities , and , where . Furthermore, we discuss the case of equality for these inequalities. We also characterize total score sequences of strong -hypertournaments