We determine the minimum hyper-Wiener index of unicyclic graphs with given number of vertices and matching number, and characterize the extremal graphs. Mathematics Subject Classification (2010): 05C12, 05C35, 05C90.

In this paper we consider the question of determining the maximum number of edges in a hamiltonian graph of order n that contains no 2-factor with more than one cycle, that is, 2-factor hamiltonian graphs. We obtain exact results for both bipartite graphs, and general graphs, and construct extremal graphs in each case. Mathematics Subject Classification (2000). Primary 05C45; Secondary 05C38.

In this paper, we study the signless Laplacian spectral radius of unicyclic graphs with prescribed number of pendant vertices or independence number. We also characterize the extremal graphs completely.

In this paper we complete the determination of the k-th (3 ≤ k ≤ bn−1 2 c) largest numbers of maximal independent sets among all quasiforest graphs of order n ≥ 8 and characterize the extremal graphs. Mathematics Subject Classification: 05C51

In this paper, we present sharp bounds for the Zagreb indices, Harary index and hyperWiener index of graphs with a given matching number, and we also completely determine the extremal graphs. © 2010 Elsevier Ltd. All rights reserved.

In this paper, we determine the maximum signless Laplacian spectral radius of all graphs which do not contain small books as a subgraph and characterize extremal graphs. addition, give an upper bound intersecting quadrangles subgraph.

A total acquisition move in a weighted graph G moves all weight from a vertex u to a neighboring vertex v, provided that before this move the weight on v is at least the weight on u. The total acquisition number, at(G), is the minimum number of vertices with positive weight that remain in G after a sequence of total acquisition moves, starting with a uniform weighting of the vertices of G. For ...

Call a graph G k-stable (with respect to some graph H) if, deleting any k edges of G, the remaining graph still contains H as a subgraph. For a fixed H, the minimum number of edges in a k-stable graph is denoted by S(k). We prove general bounds on S(k) and compute the exact value of the function S(k) for H = P4. The main result can be applied to extremal k-edge-hamiltonian hypergraphs.

Let f(n, p) be the maximum number of edges in a graph on n vertices with p perfect matchings. Dudek and Schmitt proved that there exist constants np and cp so that for even n ≥ np, f(n, p) = n 2 4 + cp; we call a graph p-extremal if it has p perfect matchings and n2 4 + cp edges. In this paper, we develop structural theorems in matching theory to study p-extremal graphs and use them in a new co...