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Discrete Mathematics
Describe Konigsberg Bridge problem
Discrete Mathematics
Show that a complete graph with n vertices has exactly n(n-1)/2 edges.
Discrete Mathematics
Hence show that the number of odd degree vertices in a graph always even.
Discrete Mathematics
Show that that sum of the degrees of the vertices in a graph is twice the number of edges in the graph.
Discrete Mathematics
Hence show that the maximum number of edges in a disconnected graph of n vertices and k components
is (n-k)(n-k+1)/2.
is (n-k)(n-k+1)/2.
Discrete Mathematics
Using the method of telescopic sums, solve
the recurrence relation : (n+1)xn-nxn-1-n/2,x0=10,n≥1
Discrete Mathematics
Find the number of distinct integer
solutions of the equation : x1+x2+ ......+x5=24
xi≥i and 1≤i≤5
Discrete Mathematics
Using generating functions, find:Sn=1+2+3+....+n
Discrete Mathematics
State the Dijkstra’s algorithm for a directed weighted graph with all non-negative edge weights.
2. Find the shortest path spanning tree for the weighted directed graph with vertices A, B, C, D, and
E given using Dijkstra’s algorithm.
Discrete Mathematics
Exponential operation: (x, y) →xy on Set of Natural numbers and set of Integers
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