Define isomorphism. Determine whether the following pair of graphs are isomorphic.
Define Hamilton cycle. How many edge disjoint Hamilton cycles exist in the complete graph with seven vertices? Also draw the graph to show these Hamilton cycles.
Draw the two simplest non-planar graphs and also mention their properties.
Prove the statement, ”Every circuit has an even number of edges in common with any cut-set”.
Define prefix code. Obtain an optimal prefix code for the message ROAD IS GOOD. Indicate the code.
From seven consonants and five vowels how many sets consisting of four different consonants and three different vowels can be formed.
Define edge vertex connectivity and edge connectivity. Give the relation between them.
In how many ways a team of 11 be chosen from 20 students of a class so that 2 particular students are always included and 5 are always excluded? [P.T.O.]
Write Kruskal’s algorithm for finding minimum spanning tree. Find the minimum spanning tree for the weighted graph shown below using Kruskal’s algorithm.
Apply Dijkstra’s algorithm to the digraph shown in figure and determine the shortest distance from vertex a to each of the other vertices in the graph.
Find the number of solutions to x1+ x 2+ x 3+ x 4=20,where x1 ≥ -5, x2 ≥ 3, x3 ≥ 0, x 4 ≥ 1.
The number of bacteria in a culture is 1000(approximately)and this number increases 250%every two hours. Use a recurrence relation to determine the number of bacteria present after one day.
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Official Gujarat Technological University (GTU) examination paper and step-by-step solutions for Graph Theory and Combinatorics (Summer 2026, B.E. · IT Engineering, Sem 7). Features complete 70-mark regular & remedial examination pattern, official marking distribution across all 5 questions, and direct 1-click official PDF download.
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