Handshaking lemma graph theory book

In more colloquial terms, in a party of people some of whom shake hands, an even number of people must have shaken an odd number of other peoples hands. Handshaking theorem in graph theory handshaking lemma. To learn the fundamental concept in graph theory and probabilities, with a sense of some of its modern application. This may not be true when the simple graphs are considered. The result first appeared in eulers 1736 paper on the seven bridges of konigsberg and is also known as the handshaking lemma thats because another way of formulating the property is that the number of people that have shaken hands an odd number of times is even. I thechromatic numberof a graph is the least number of colors needed to color it. Degree is a number of edges associated with a node. Handshaking lemma in graph theory basically says that the degree sum is equal to twice the number of edges. In graph theory, handshaking theorem or handshaking lemma or sum of degree of vertices theorem states that sum of degree of all vertices is twice the number of edges contained in it. If you have an undirected graph, and if you compute the sum of degrees of all its vertices, then what you get is exactly twice the number of edges, right.

As we can easily verify, the graph shown above satisfies this property. Excel books private limited a45, naraina, phasei, new delhi110028 for lovely professional university phagwara. Handshaking lemma, theorem, proof and examples youtube. The handshaking lemma is a consequence of the degree sum formula also sometimes called the handshaking lemma how is handshaking lemma useful in tree data structure. Handshaking lemma in graph theory the crazy programmer. Graph coloring i acoloringof a graph is the assignment of a color to each vertex so that no two adjacent vertices are assigned the same color. Graph theory 02 handshaking lemma complete graph bipartite graph discrete mathematics lectures duration. Handshaking lemma and existence of the graph mathematics. That is if the degree sum is even then a graph exists with that corresponding degree sequence. Hello everyone, today we will see handshaking lemma associated with graph theory. Handshaking lemma article about handshaking lemma by the.