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In graph theory, a regular graph is a graph where each vertex has the same number of neighbors; i.e. every vertex has the same degree or valency. A regular directed graph must also satisfy the stronger condition that the indegree and outdegree of each internal vertex are equal to each other. [1]
A graph with 6 vertices and 7 edges. In mathematics and computer science, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects.
Its authors have divided Elementary Number Theory, Group Theory and Ramanujan Graphs into four chapters. The first of these provides background in graph theory, including material on the girth of graphs (the length of the shortest cycle), on graph coloring, and on the use of the probabilistic method to prove the existence of graphs for which both the girth and the number of colors needed are ...
In the mathematical field of graph theory, a distance-regular graph is a regular graph such that for any two vertices v and w, the number of vertices at distance j from v and at distance k from w depends only upon j, k, and the distance between v and w. Some authors exclude the complete graphs and disconnected graphs from this definition.
Such a strongly regular graph is denoted by srg(v, k, λ, μ). Its complement graph is also strongly regular: it is an srg(v, v − k − 1, v − 2 − 2k + μ, v − 2k + λ). A strongly regular graph is a distance-regular graph with diameter 2 whenever μ is non-zero. It is a locally linear graph whenever λ = 1.
Balakrishnan was born in Mangilao, Guam [3] to Narayana and Shizuko Balakrishnan; her father is a professor of chemistry at the University of Guam. [4] [5] As a junior at Harvest Christian Academy, Balakrishnan won an honorable mention in the 2001 Karl Menger Memorial Award competition, for the best mathematical project in the Intel International Science and Engineering Fair.
This is a 3-regular graph with 56 vertices and 84 edges, named after Felix Klein. It is Hamiltonian, has chromatic number 3, chromatic index 3, radius 6, diameter 6 and girth 7. It is also a 3-vertex-connected and a 3-edge-connected graph. It has book thickness 3 and queue number 2. [1]
They considered an operation called a 2-lift that takes a -regular graph with vertices and a sign on each edge, and produces a new -regular graph ′ on vertices. Bilu & Linial conjectured that there always exists a signing so that every new eigenvalue of G ′ {\displaystyle G'} has magnitude at most 2 d − 1 {\displaystyle 2{\sqrt {d-1}}} .
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