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Prove that a simple graph is connected if and only if it has a spanning tree.
Ans: First assume that a simple graph G has a spanning tree T. T consists of every node of G. By the definition of a tree, there is a path among any two nodes of T. As T is a subgraph of G, there is a path among each pair of nodes in G. Hence G is connected.
Here now let G is connected. If G is a tree then nothing to prove. If G is not a tree, it must consist of a simple circuit. Let G has n nodes. We can choose (n - 1) arcs from G in such type of a way that they not form a circuit. It results into a subgraph comprising all nodes and only (n - 1) arcs. So by definition this subgraph is a spanning tree.
An IVP or Initial Value Problem is a differential equation with an appropriate number of initial conditions. Illustration 3 : The subsequent is an IVP. 4x 2 y'' + 12y' +
Give the introduction to Ratios and Proportions? A ratio represents a comparison between two values. A ratio of two numbers can be expressed in three ways: A ratio of "one t
FIND PRODUCT (-41)*(102)
A well-known simple model, applicable for analysing boom-bust cycles in agriculture, but extendable to analysing boom-bust cycles in many different areas of economics is the hog cy
Find the largest possible positive integer that will divide 398, 436, and 542 leaving remainder 7, 11, 15 respectively. (Ans: 17) Ans: The required number is the HCF of the n
Memphis, Tennessee, and New Orleans, Louisiana, lie approximately on the same meridian. Memphis has latitude 35°N and New Orleans has latitude 30°N. Find the distance between these
Here we have considered the following points. 1. Mathematics is omnipresent, powerful and beautiful. 2. Mathematics is useful in all spheres of life. 3. Mathematics can al
korda ab e ndan rrethin me qender o ne dy harqe njeri prej tyre eshte sa trefishi i tjetrit gjeni masat e harqeve dhe masat e trekendeshit aob
63*789
Eliment t from following equations v=u+at s=ut+1/2at^2
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