Minimum Spanning Tree may be or may not be unique. It depends on the weight of the edge. If all the weight are unique then we can have a unique …

Read More »## Graph Theory and Applications

Graph Theory Graph theory is the study of graphs which are mathematical structures used to model pairwise relations between objects. Applications of Graph Theory Development of graph algorithm. Chemical Identification. …

Read More »## Euler Tour – Euler Trail – Hamiltonian Cycle all graph

Euler Trail but not Euler Tour Conditions: At most 2 odd degree (number of odd degree <=2) of vertices. Start and end nodes are different. Euler Tour but not Euler …

Read More »## Euler Tour – Euler Trail

Cycle In a graph, cycle is a tour with start and end with same node. Trail Trail is a path where every edge (line) is traversed exactly once and start …

Read More »## Hamilton Path and Hamilton Cycle

Hamilton Path A Hamilton path is a path in a graph that visits every node (vertices) exactly once in a way that start and end node is different. Hamilton Cycle …

Read More »## Star Graph – Face – Planar Embedding

Star Graph Star graph is a complete bipartite graph K, a tree with internal node and K leaves. Fig: Star Graph Face In a planar drawing of a graph, the …

Read More »## Tree – Tree Properties and Minimum Spanning tree

Tree A connected acyclic graph is called a tree. Tree Properties Any connected sub-graph is a tree. There is a unique simple path between every pair of vertices. Adding an …

Read More »## Chromatic Number and applications

Chromatic Number Chromatic Number of a graph is the smallest number of colors needed to color the vertices so that no two adjacent vertices share the same color. Application of …

Read More »## Walk – Cycle – Connectivity – Tournament Graph

Walk A walk is a sequence of vertices. Cycle Cycle is a closed walk in a graph, a closed sequence of vertices. Connectivity A graph is said to be connected …

Read More »## Diagraph – Directed Walk – Directed acyclic graph (DAG)

Diagraph A graph with directed edges is called a directed graph or diagraph. Fig: A 3 node directed graph Directed Walk A directed walk (or Walk) in a directed graph …

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