A very well edited bookĭiscrete Math has applications in many areas including computer science, economics, etc. It is preparing the students to take more proof intensive courses such as Linear Algebra. This really helps the students to understand the material well. He goes through the proofs in much more details than most of the other books on this topic. However, the approach taken by this author is excellent. Many students find them to be hard to comprehend. Discrete Math is usually the first course where the students come across theorems and proofs. My students also liked the fact that they did not have to pay any money to use the book. I used this book for my course on "Computational Discrete Mathematics". It provides a good motivation for the topic that is going to be covered. The "investigate" part for each concept is an excellent approach. These are the topics normally covered in any typical discrete math course. This book covers all the important topics such as set theory, logic, counting techniques, number theory, graph theory etc. Reviewed by Nachimuthu Manickam, Professor, DePauw University on 12/18/20 Journalism, Media Studies & Communications.(1962), "On realizability of a set of integers as degrees of the vertices of a linear graph. Diestel, Reinhard (2005), Graph Theory (3rd ed.), Berlin, New York: Springer-Verlag, ISBN 978-3-4.^ Deza, Antoine Levin, Asaf Meesum, Syed M."Topological impact of negative links on the stability of resting-state brain network". ^ Saberi M, Khosrowabadi R, Khatibi A, Misic B, Jafari G (January 2021).
Physica A: Statistical Mechanics and Its Applications. "Degree correlations in signed social networks".
By Brooks' theorem, any graph G other than a clique or an odd cycle has chromatic number at most Δ( G), and by Vizing's theorem any graph has chromatic index at most Δ( G) + 1.A functional graph is a special case of a pseudoforest in which every vertex has outdegree exactly 1. A directed graph is a directed pseudoforest if and only if every vertex has outdegree at most 1.If it has 0 vertices of odd degree, the Eulerian path is an Eulerian circuit. An undirected, connected graph has an Eulerian path if and only if it has either 0 or 2 vertices of odd degree.Similarly, a bipartite graph in which every two vertices on the same side of the bipartition as each other have the same degree is called a biregular graph.
If each vertex of the graph has the same degree k, the graph is called a k-regular graph and the graph itself is said to have degree k.A vertex with degree n − 1 in a graph on n vertices is called a dominating vertex.This terminology is common in the study of trees in graph theory and especially trees as data structures. The degree of a vertex v is a pendant edge.
In graph theory, the degree (or valency) of a vertex of a graph is the number of edges that are incident to the vertex in a multigraph, a loop contributes 2 to a vertex's degree, for the two ends of the edge. A graph with a loop having vertices labeled by degree