Discrete Mathematics Tutorial Problems PDF

A picture containing text, font, logo, brand Description automatically generated **Department of Mathematics** **24MT1002: Discrete Mathematics** **I/IV-B. Tech-(ODD Sem), Academic Year: 2024-2025** ***TUTORIAL PROBLEMS-CO-4*** ***TUTORIAL-10*** 1. Is there a simple graph with degree sequence...

A picture containing text, font, logo, brand Description automatically generated **Department of Mathematics** **24MT1002: Discrete Mathematics** **I/IV-B. Tech-(ODD Sem), Academic Year: 2024-2025** ***TUTORIAL PROBLEMS-CO-4*** ***TUTORIAL-10*** 1. Is there a simple graph with degree sequence (1,1,3,3,3,4,6,7)? Justify your answer. 2. Determine whether the following graph is a simple graph or multigraph, and obtain the adjacency matrix. a.  A picture containing circle, sketch, drawing, white Description automatically generated b 3. Draw a graph with the adjacency matrix [\$\\begin{bmatrix} \\begin{matrix} 1 & 1 \\\\ 0 & 0 \\\\ \\end{matrix} & \\begin{matrix} 1 & 0 \\\\ 1 & 0 \\\\ \\end{matrix} \\\\ \\begin{matrix} 1 & 0 \\\\ 1 & 1 \\\\ \\end{matrix} & \\begin{matrix} 1 & 0 \\\\ 1 & 0 \\\\ \\end{matrix} \\\\ \\end{bmatrix}\$]{.math.inline} with respect to the ordering of the vertices a, b, c, d. 4. Check whether the graph H displayed are bipartite or not?  5. Check whether the graphs are isomorphic or not? a i. A picture containing line Description automatically generated B. ***TUTORIAL-11*** 1. which of the following graphs have Euler circuit, then construct such graph if exist. A picture containing line, design Description automatically generated  2. Which of the following graphs have Hamilton circuit or Hamilton path, and then construct such graph if exist. A picture containing line, diagram Description automatically generated  3. Which of these non-planar graphs have the property that the removal of any vertex and all edges incident with that vertex produces with planar graph? a\) K~6~ b) K~3,\ 3~ 4. Determine whether the given graph is planar. If so, draw it so that no edges cross. a. A picture containing line Description automatically generatedb.  5. Determine all spanning trees of the graph G shown in the following Figure. b. A picture containing circle, diagram, line, screenshot Description automatically generated ***TUTORIAL-12*** 1. Construct all possible spanning trees of the graph H shown in the following Figure.  2. Apply Kruskal's Algorithm to construct the minimum spanning tree (MST) from the following graph. A picture containing line, diagram, circle Description automatically generated 3. Apply Kruskal's Algorithm to construct the minimum spanning tree (MST) from the following graph.