1-Factors of point determining graphs

Enumeration of point-determining graphs

Point-determining graphs are graphs in which no two vertices have the same neighborhoods, co-point-determining graphs are those whose complements are point-determining, and bi-point-determining graphs are those both point-determining and co-point-determining. Bicolored point-determining graphs are point-determining graphs whose vertices are properly colored with white and black. We use the comb...

Graphs with 1-factors

In this paper it is shown that if G is a connected graph of order 2n (n> 1) not containing a 1-factor, then for each k, Kk^n, there exists an induced, connected subgraph of order 2k which also fails to possess a 1-factor. Several other sufficient conditions for a graph to contain a 1-factor are presented. In particular, it is seen that the connected even order line graphs and total graphs alway...

The 1-factors of Oriented Graphs

1. Introduction. A graph G consists of a set 7 of elements called vertices together with a set E of elements called edges, the two sets having no element in common. With each edge there are associated either one or two vertices called its ends. In this paper we consider only graphs in which each edge has two distinct ends. We call such a graph oriented if one end of each edge is distinguished a...

The lower bound for the number of 1-factors in generalized Petersen graphs

‎In this paper‎, ‎we investigate the number of 1-factors of a‎ ‎generalized Petersen graph $P(N,k)$ and get a lower bound for the‎ ‎number of 1-factors of $P(N,k)$ as $k$ is odd‎, ‎which shows that the‎ ‎number of 1-factors of $P(N,k)$ is exponential in this case and‎ ‎confirms a conjecture due to Lovász and Plummer (Ann‎. ‎New York Acad‎. ‎Sci‎. ‎576(2006)‎, ‎no‎. ‎1‎, ‎389-398).

Some factorizations of graphs into C5-Factors and 1-Factors