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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 …

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. …

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 …

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 …

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 …

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 …

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 …

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 …

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 …

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 …