A graph is called perfect matching compact (briefly, PM -compact), if its perfect matching graph is complete. Matching-covered PM -compact bipartite graphs have been characterized. In this paper, we show that any PM -compact bipartite graph G with δ(G) ≥ 2 has an ear decomposition such that each graph in the decomposition sequence is also PM -compact, which implies that G is matching-covered.

Let G be a k-connected graph of order n. In [1], Bondy considered a degree sum condition for a graph to have a hamiltonian cycle, say, to be covered by one cycle. He proved that if σk+1(G) > (k+1)(n− 1)/2, then G has a hamiltonian cycle. On the other hand, concerning a degree sum condition for a graph to be covered by two cycles, Enomoto et al. [4] proved that if k = 1 and σ3(G) ≥ n, then G can...

this survery investigated the secondary school students attitude regarding parent- adolescent inter-relationships. the study covered 19 town districts in tehran.   following a multi-stage process 150 girls and boys attending secondary school with an age range of 13-15 years were selected randomly.   a two parts questionnaire was developed. the first part covered information on personal and soci...

A maximum stable set in a graph G is a stable set of maximum cardinality. S is a local maximum stable set of G, and we write S ∈ Ψ(G), if S is a maximum stable set of the subgraph induced by S ∪N(S), where N(S) is the neighborhood of S. Nemhauser and Trotter Jr. [20], proved that any S ∈ Ψ(G) is a subset of a maximum stable set of G. In [12] we have shown that the family Ψ(T ) of a forest T for...

Let G = (V,E) be a graph. If G is a König graph or if G is a graph without 3-cycles and 5-cycles, we prove that the following conditions are equivalent: ∆G is pure shellable, R/I∆ is Cohen-Macaulay, G is an unmixed vertex decomposable graph and G is well-covered with a perfect matching of König type e1, . . . , eg without 4-cycles with two ei’s. Furthermore, we study vertex decomposable and she...

Combining the concept of a fractional ( g , f )-covered graph with that ID-( )-factor-critical graph, we define covered graph. This paper reveals relationship between some parameters and existence graphs. A sufficient condition for being is presented. In addition, demonstrate sharpness main result in this by constructing special class. Furthermore, other parameters(such as binding number, tough...

If sk denotes the number of stable sets of cardinality k in the graph G,

A matching covered graph is a nontrivial connected graph in which every edge is in some perfect matching. A matching covered graph G is near-bipartite if it is nonbipartite and there is a removable double ear R such that G−R is matching covered and bipartite. In 2000, C. Little and I. Fischer characterized Pfaffian near-bipartite graphs in terms of forbidden subgraphs [3]. However, their charac...