Written for mathematicians working with the theory of graph spectra, this (primarily theoretical) book presents relevant results considering the spectral properties of regular graphs. The book begins with a short introduction including necessary terminology and notation. The author then proceeds with basic properties, specific subclasses of regular graphs (like distance-regular graphs, strongly regular graphs, various designs or expanders) and determining particular regular graphs. Each chapter contains detailed proofs, discussions, comparisons, examples, exercises and also indicates possible applications. Finally, the author also includes some conjectures and open problems to promote further research.
Contents Spectral properties Particular types of regular graph Determinations of regular graphs Expanders Distance matrix of regular graphs
Frequently asked questions
Yes, you can cancel anytime from the Subscription tab in your account settings on the Perlego website. Your subscription will stay active until the end of your current billing period. Learn how to cancel your subscription.
At the moment all of our mobile-responsive ePub books are available to download via the app. Most of our PDFs are also available to download and we're working on making the final remaining ones downloadable now. Learn more here.
Perlego offers two plans: Essential and Complete
Essential is ideal for learners and professionals who enjoy exploring a wide range of subjects. Access the Essential Library with 800,000+ trusted titles and best-sellers across business, personal growth, and the humanities. Includes unlimited reading time and Standard Read Aloud voice.
Complete: Perfect for advanced learners and researchers needing full, unrestricted access. Unlock 1.4M+ books across hundreds of subjects, including academic and specialized titles. The Complete Plan also includes advanced features like Premium Read Aloud and Research Assistant.
Both plans are available with monthly, semester, or annual billing cycles.
We are an online textbook subscription service, where you can get access to an entire online library for less than the price of a single book per month. With over 1 million books across 1000+ topics, we’ve got you covered! Learn more here.
Look out for the read-aloud symbol on your next book to see if you can listen to it. The read-aloud tool reads text aloud for you, highlighting the text as it is being read. You can pause it, speed it up and slow it down. Learn more here.
Yes! You can use the Perlego app on both iOS or Android devices to read anytime, anywhere — even offline. Perfect for commutes or when you’re on the go. Please note we cannot support devices running on iOS 13 and Android 7 or earlier. Learn more about using the app.
Yes, you can access Regular Graphs by Zoran Stanić in PDF and/or ePUB format, as well as other popular books in Mathematics & Counting & Numeration. We have over one million books available in our catalogue for you to explore.
Here we give a survey of the main graph-theoretic terminology, notation and necessary results. The presentation is separated into three sections. In the first two we deal with graph structure and give some observations including statistical data on regular graphs. In the third section we focus on the adjacency matrix and the corresponding spectrum.
Since all parts of this chapter can be found in numerous sources, by the assumption that the reader is familiar with most of the concepts presented, we orientate to a brief but very clear and intuitive exposition. More details are given in the introductory chapter of our previous book [290].
1.1Terminology and notation
Vertices and edges
Let G be a finite undirected simple graph (so, without loops or multiple edges). We denote its set of vertices (resp. edges) by V or V(G) (resp. E or E(G)). In addition, we assume that
. The quantities n = |V| and m = |E| are called the order and the size of G, respectively. Two vertices u and v are adjacent (or neighbours) if they are joined by an edge. In this case we write u ~ v and say that the edge uv is incident with vertices u and v. Similarly, two edges are adjacent if they are incident with a common vertex.
The set of neighbours (or the neighbourhood) of a vertex v is denoted N(v). The closed neighbourhood of v is denoted N[v] (= {v} ∪ N(v)).
Two graphs G and H are said to be isomorphic if there is a bijection between sets of their vertices which respects adjacencies. If so, then we write G ≅ H. Observe that the graphs illustrated in Figure 1.1 are isomorphic. In particular, an automorphism of a graph is an isomorphism to itself.
The degree dv of a vertex v is the number of edges incident with it. The minimal and the maximal vertex degrees in a graph are denoted δ and Δ, respectively. A vertex of degree 1 is called an endvertex or a pendant vertex.
We say that a graph G is regular of degree r if all its vertices have degree r. If so, then G is refe...
