WebDec 30, 2024 · 1. I want to find $\alpha (G)$ that is vertex independence number (maximum number of vertices, no two of which are adjacent) and $\beta (G)$ that is edge covering number (minimum number of vertices that cover all edges of G) of this graph: I've found that $\alpha (G)=2$. And there is theorem that says: $\alpha (G)+\beta (G)=n$. WebHere, M 1, M 2, M 3 are minimal line coverings, but M 4 is not because we can delete {b, c}.. Minimum Line Covering. A minimal line covering with minimum number of edges is called a minimum line covering of graph G. It is also called smallest minimal line covering.. Every minimum edge cover is a minimal edge cove, but the converse does not …
Minimum Edge Cover and Edge Covering Number Graph …
WebJan 10, 2014 · Corpus ID: 25232367; Lower bounds for algebraic connectivity of graphs in terms of matching number or edge covering number @article{Xu2014LowerBF, title={Lower bounds for algebraic connectivity of graphs in terms of matching number or edge covering number}, author={Jing Xu and Yi-Zheng Fan and Ying-Ying Tan}, … WebMar 27, 2024 · A generalization of edge cover. Suppose we are given a general (connected) undirected graph G = ( V, E). An EDGE COVER asks a set S ⊆ E of the minimum number of edges, such that each vertex v ∈ V is incident to at least one edge s ∈ S. Note that this is solvable in polynomial time. Now I'd like to generalize this problem to … the wale español latino
Complete bipartite graph - Wikipedia
WebAug 23, 2024 · A minimal line covering with minimum number of edges is called a minimum line covering of 'G'. The number of edges in a minimum line covering in 'G' is called the line covering number of 'G' (α 1). Example. In the above example, C 1 and C 2 are the minimum line covering of G and α 1 = 2. Every line covering contains a minimal … WebMay 15, 2014 · Keywords: clique, clique cover, clique covering number. 1 Introduction. Covering theory in graphs has been studied by a number of graph theorists. Various types of covering a graph such as vertex covering, edge covering, clique 4302 Frederick S. Gella and Rosalio G. Artes, Jr. covering, tree covering, forest covering, and path triple … WebJan 9, 2014 · Xu, Fan and Tan [15] determined the lower bounds for the algebraic connectivity in terms of matching number or edge covering number. In this paper, we … the wale online sa prevodom