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Branches of Network Topology:

1. Physical Topology: Deals with the physical layout of nodes and devices in a network and how they are connected.

2. Logical Topology: Focuses on how data flows within the network and the logical paths used for communication.

Topics in Network Topology:

1. Bus Topology: A type of physical topology where all devices are connected to a single communication line.

2. Star Topology: Involves a central hub that connects all devices in the network.

3. Ring Topology: Forms a closed loop where each device is connected to two others.

4. Mesh Topology: Each device is connected to every other device in the network, creating redundant paths.

5. Tree Topology: Combines the characteristics of bus and star topologies, forming a hierarchical structure.

Theorems in Network Topology:

1. Euler’s Formula: Relates the number of vertices, edges, and faces in a planar graph.

2. Cut-Set Theorem: Relates the number of cut-sets and bridges in a network.

3. Menger’s Theorem: Provides conditions for the existence of multiple disjoint paths between two nodes.

4. Kuratowski’s Theorem: Helps identify non-planar graphs by characterizing forbidden subgraphs.

5. Jordan Curve Theorem: Describes the properties of curves on a 2-dimensional surface and their separation of points.

6. Four Color Theorem: States that any map can be colored using only four colors, so that no two adjacent regions have the same color.

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