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From the First Principle of Counting we have arrived at the commutativity of addition, which was expressed in convenient mathematical notations as a + b = b + a. The Principle itself…
A rooted tree is a tree with a special vertex labelled as the “root” the of tree. The root serves as a…
Chromatic number of a graph is the minimum value of kk for which the graph is k-colorablek-colorable. In other words, it is the minimum…
Not all graphs are planar. If there are too many edges and too few vertices, then some of the edges…
When is it possible to draw a graph so that none of the edges cross? If this is possible, we say the…
Certain graph problems deal with finding a path between two vertices such that each edge is traversed exactly once, or…
An Euler graph may be defined as- Euler Graph Example- The following graph is an example of an Euler graph-…
Walks Definition: For a graph G=(V(G),E(G)), a Walk is defined as a sequence of alternating vertices and edges such as v0,e1,v1,e2,…,ek,vk where each edge ei={vi−1,vi}. The Length of this…
Definition: A Subgraph S of a graph G is a graph whose vertex set V(S) is a subset of the vertex set V(G), that is V(S)⊆V(G), and whose edge set E(S) is…
Graphs come with various properties which are used for characterization of graphs depending on their structures. These properties are defined…
A graph is a diagram of points and lines connected to the points. It has at least one line joining…
In this chapter, we will cover a few standard examples to demonstrate the concepts we already discussed in the earlier…
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