Cacti with the maximum Merrifield–Simmons index and given number of cut edges

Ela on the Estrada Index of Graphs with given Number of Cut Edges

Let G be a simple graph with eigenvalues λ1, λ2, . . . , λn. The Estrada index of G is defined as EE(G) = ∑ n i=1 ei . In this paper, the unique graph with maximum Estrada index is determined among connected graphs with given numbers of vertices and cut edges.

On the Estrada index of graphs with given number of cut edges

Let G be a simple graph with eigenvalues λ1, λ2, . . . , λn. The Estrada index of G is defined as EE(G) = ∑ n i=1 ei . In this paper, the unique graph with maximum Estrada index is determined among connected graphs with given numbers of vertices and cut edges.

The Maximum Number of Edges in a Strongly Multiplicative Graph

On the maximum number of edges in a hypergraph with given matching number

The aim of the present paper is to prove that the maximum number of edges in a 3-uniform hypergraph on n vertices and matching number s is max {(3s+ 2 3 ) , ( n 3 ) − ( n− s 3 )} for all n, s, n ≥ 3s+ 2.

The Signless Laplacian or Adjacency Spectral Radius of Bicyclic Graphs with Given Number of Cut Edges

LetB(n, r) be the set of all bicyclic graphs with n vertices and r cut edges. In this paper we determine the unique graph with maximal adjacency spectral radius or signless Laplacian spectral radius among all graphs in B(n, r).