**ELEMENTS OF GRAPH THEORY**

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**BRANCH AND NODE**

**A branch which represents a Circuit element is a line joining two nodes and a nodes is defined as a common point at which two or more Branches meet together.**

**GRAPH. A liner graph or simply a graph is defined as a collection of node and branches. It's shows the geometrical interconnection of the elements of a network. A graph is connected and of there is a path directly or indirectly between every pairs of nodes. The Circuit of a graph have the following properties.**

**1) The maximum number of branches in a Circuit will be equal to the number of nodes.**

**2) There are exactly two paths between any pair of node in a Circuit.**

**3) There are at least two branches.**

**A network N and the corresponding graph G in Fig.** (B) (C)

**Undirected graph of Directed ooriented**

**the Network given**

**in graph of Network**

**fig. Given in fig.**

*Each branch or edge of the graph in fig. Carries and arrow to indicate orientation. A graph whose branches are oriented is called a directed or oriented graph as fig.*

*Otherwise graph is indirected as fig.*

__PATH__

*A path is a improper subgraph such that,*

*a) At the terminating nodes, only one branch is incident, and*

*b) At the remaining nodes, two branches are incident.*

__REQUIREMENTS FOR THE DUAL NETWORKS.__1

**) Number of mashes in a given Network must be equal to the number of nodes of a dual Network.**

**3) Impedance of branch common the two mashes must be equal to the the admittance between two nodes in the equal Network.**

**4) Voltage source common to both the loops must be represented as Current source between two nodes.**

**5) The switch opening at t = 0 in the given Network must be shown as a switch closing at t = 0 in the dual Networks.**

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