Hello Readers, Hope you all are doing well. Today, I am going to write the proof of Cayley's Theorem which counts the number of labelled trees. Cayley's Theorem is very important topic in graph theory. If you study Graph theory and don't know Cayley's theorem then it would be very surprising. Ok, So lets start … Continue reading Cayley’s Theorem: Enumeration of Graphs

# Five Color Theorem: Proof

Hello Readers, Have a nice day! In this post, i am writing on the proof of famous theorem known as "Five Color Theorem". Hope, you understood this proof. Thank you Stay Connected, Stay learned Dr. Namita Tiwari

# Decomposition Theorem to find Chromatic polynomial

Hello Readers, Hope you are doing well. This post is based on Decomposition Theorem that is very important to find out the chromatic Polynomials of given finite graphs. Let us understand this theorem with some examples. Hope you understood. Thank you for reading. Stay Connected, Stay learned. Dr. Namita Tiwari

# Chromatic Polynomial of some specific Graphs

Hello Readers Today, I am writing on a very important topic of Graph theory, i.e. "Chromatic Polynomial" that tells us the total number of different ways to color properly a given graph G using λ or fewer colors. In this post i have discussed chromatic polynomials of some specific Graphs like null graph, path, complete … Continue reading Chromatic Polynomial of some specific Graphs

# Pseudo Graph

Hello Readers Hope you are doing well. Today i am writing a short note on Pseudo-graph. Generally people get confused about the definition of pseudo-graph. Pseudo word refers to spurious i.e. `mithya'. Some authors say that a graph without multiple edges and self-loops is called pseudo-graph while others produce the examples of pseudo-graph as a … Continue reading Pseudo Graph

# Pigeonhole Principle

Hello Readers Hope you are doing well. Today i am writing on very important mathematical tool based on combinatorics that is pigeonhole principle. What actually `Pigeonhole' word refers? It refers to the square boxes or holes utilized to place pigeons in the united states. Inspiring by this concept, a mathematical principle was introduced in 1834 by a … Continue reading Pigeonhole Principle

# Every tree has either one or two center

Every tree has either one or two centers