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Prove that a graph G is connected and only if it has a spanning tree?
Proving this is simple. First, you prove that G has a spanning tree, it is connected, which is pretty obvious - a spanning tree itself is already a connected graph on the vertex set V(G), thus G which contains it as a spanning sub graph is obviously also connected. Second, you prove that if G is connected, it has a spanning tree. If G is a tree itself, then it must "contain" a spanning tree. If G is connected and not a tree, then it must have at least one cycle. I don't know if you know this or not, but there is a theorem stating that an edge is a cut-edge if and only if it is on no cycle (a cut-edge is an edge such that if you take it out, the graph becomes disconnected). Thus, you can just keep taking out edges from cycles in G until all that is left are cut-gees. Since you did not take out any cut-edges, the graph is still connected; since all that is left are cut-edges, there are no cycles. A connected graph with no cycles is a tree. Thus, G contains a spanning tree. Therefore, a graph G is connected if and only if it has a spanning tree!
What is a divisor graph?
Let S be a finite, non-empty set of positive integers. The divisor graph G(S) of S has S as its vertex set, and two distinct vertices i and j are adjacent if and only if either idivides j or j divides i. Let G be a simple graph. Then G is called a divisor graph if G is isomorphic to G(S) for some non-empty, finite set S of positive integers.REFERENCE :S. Ganesan, D. Uthayakumar, Corona of Bipartite Graphs with Divisor GRaphs Produce New Divosor Graphs,Bulletin of Kerala Mathematics AssociationVol.9, No.1, (2012, June) 219-226
What is cyclomatic number of a graph is called?
cyclomatic number of a graph is e.n+1 where e is number of edge of graph and n is number of node in graoh g
How many g are in 320kg?
1 kg = 1,000 g so 320 kg = 320*1000 = 320,000 g. Simple!1 kg = 1,000 g so 320 kg = 320*1000 = 320,000 g. Simple!1 kg = 1,000 g so 320 kg = 320*1000 = 320,000 g. Simple!1 kg = 1,000 g so 320 kg = 320*1000 = 320,000 g. Simple!
How do you graph fx-x-1 3 gx-x-2 and hx -3x-1?
graph G(x)=[x]-1
