Discrete Mathematics

Daffodil International University Faculty of Science, Information & Technology Department of Computing and Information System MidTerm Semester Examination, Fall-2026 Course Code: CIS123 Course Title: Discrete Mathematics Level: 1 Term: 3 Section: ALL Exam Duration: 1.5 Hours Marks: 25 Answer ALL Questions [The figures in the right margin indicate the full marks and corresponding course outcomes. 1. a. Demonstrate your knowledge to draw the graph: C5, K3,2, regular graph and multigraph. (4 Marks, CO2) 1. b. i. Find the in-degree and out-degree of the given graph in fig 02 [Figure: Directed graph Fig 02 with vertices 1 through 6] (2 Marks) ii. Represent the directed graph in fig. 02 using adjacency list graph representation method. (2 Marks) iii. Prove hand shaking theory using an example by yourself of pseudo graph. (2 Marks) iv. Represent your graph in ques. 1.b(iii) using adjacency matrix of graph representation method. (2 Marks) 2. a. Determine the graph G is bipartite or not. Justify your answer. [Figure: Graph: G] (3 Marks, CO3) 2. b. Determine the graph H and I are isomorphic or not. Justify your answer using all steps. [Figure: Graph: H and Graph: I] (5 Marks) 2. c. I. Determine whether the given graph 'A' has a Hamilton circuit and path or not. (Mention rules and path if it has) [Figure: Graph: A] (2.5 Marks) II. Determine whether the given graph 'B' has a Euler circuit and path or not. (Mention rules and path if it has) [Figure: Graph: B] (2.5 Marks) Allah Hafez !