📘 Topic: Graph Theory (Part of Network Theorems / Network Analysis)
1. In a connected graph, the number of twigs is equal to:
- a) Number of nodes
- b) Number of branches
- c) (n – 1), where n is the number of nodes ✔️
- d) (b – n + 1), where b is branches, n is nodes
Explanation: Twigs form the tree of the graph and a tree always has (n - 1) branches, where n is the number of nodes.
2. The number of fundamental loops in a graph is given by:
- a) Number of nodes
- b) Number of branches
- c) (b – n + 1) ✔️
- d) (n – 1)
Explanation: The number of independent loops in a connected graph = b – n + 1.
3. A tree in graph theory is:
- a) A graph with loops
- b) A connected graph with no closed path ✔️
- c) A disconnected graph
- d) A graph with self-loops
Explanation: A tree is a subgraph that connects all nodes without forming any loops.
4. A co-tree consists of:
- a) Only loops
- b) Only nodes
- c) Links (chords) ✔️
- d) Twigs
Explanation: Co-tree is formed by the remaining branches (links/chords) not part of the tree.
5. In a planar graph, the number of independent KVL equations is equal to:
- a) Number of nodes
- b) Number of loops
- c) Number of twigs
- d) Number of meshes ✔️
Explanation: Each mesh corresponds to an independent KVL equation.
6. A loop in graph theory is:
- a) A path that starts and ends at the same node ✔️
- b) A path that connects two different nodes
- c) A subgraph with no nodes
- d) A disconnected path
Explanation: A loop is a closed path in which no node is repeated except the starting/ending one.
7. The incidence matrix of a graph is:
- a) A square matrix
- b) A matrix that shows relation between branches and nodes ✔️
- c) A matrix that shows loops and nodes
- d) A matrix with only zero elements
Explanation: Incidence matrix is used to represent the node-branch relationship in a graph.
8. Which of the following matrices helps in loop analysis?
- a) Incidence matrix
- b) Tie-set matrix ✔️
- c) Cut-set matrix
- d) Identity matrix
Explanation: Tie-set matrix is used for writing KVL equations in loop analysis.
9. If a graph has 5 nodes and 7 branches, the number of independent loops is:
- a) 2
- b) 3 ✔️
- c) 5
- d) 7
Explanation: Independent loops = b – n + 1 = 7 – 5 + 1 = 3
10. Which matrix is useful in node voltage method of analysis?
- a) Tie-set matrix
- b) Cut-set matrix ✔️
- c) Incidence matrix
- d) Admittance matrix
Explanation: Cut-set matrix is used for KCL-based node voltage analysis.
📌 Summary:
- Focus on twig = (n–1) and loops = (b–n+1) formulas.
- Know definitions of tree, loop, link, co-tree, incidence, tie-set, cut-set.
- Use these concepts in solving KCL, KVL, mesh, and nodal equations in network analysis.