By Lowell W. Beineke, Robin J. Wilson, Ortrud R. Oellermann
The speedily increasing sector of structural graph concept makes use of principles of connectivity to discover quite a few points of graph concept and vice versa. It has hyperlinks with different parts of arithmetic, corresponding to layout conception and is more and more utilized in such parts as desktop networks the place connectivity algorithms are a tremendous function. even though different books disguise elements of this fabric, none has a equally vast scope. Ortrud R. Oellermann (Winnipeg), across the world known for her massive contributions to structural graph thought, acted as educational advisor for this quantity, assisting form its insurance of key themes. the result's a set of 13 expository chapters, every one written by way of stated specialists. those contributions were conscientiously edited to reinforce clarity and to standardise the bankruptcy constitution, terminology and notation all through. An introductory bankruptcy information the history fabric in graph concept and community flows and every bankruptcy concludes with an in depth checklist of references.
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Submit yr word: First released in 2008
Networks of relationships aid ascertain the careers that individuals opt for, the roles they receive, the goods they purchase, and the way they vote. the various facets of our lives which are ruled by way of social networks make it serious to appreciate how they influence habit, which community buildings tend to emerge in a society, and why we manage ourselves as we do.
In Social and fiscal Networks, Matthew Jackson bargains a complete advent to social and monetary networks, drawing at the newest findings in economics, sociology, desktop technology, physics, and arithmetic. He offers empirical history on networks and the regularities that they express, and discusses random graph-based versions and strategic versions of community formation. He is helping readers to appreciate habit in networked societies, with a close research of studying and diffusion in networks, determination making through people who are inspired via their social pals, online game concept and markets on networks, and a bunch of similar topics. Jackson additionally describes the various statistical and modeling strategies used to investigate social networks. each one bankruptcy contains routines to assist scholars of their research of the way networks function.
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Extra info for Topics in Structural Graph Theory
Aharoni strengthened their result when he showed the conjecture to be true for all graphs that contain no infinite path  and for all countable graphs . 3. Edge-connectivity The vertex versions of Menger’s theorem discussed in Section 2 have edge analogues that we briefly describe here. Let v and w be two vertices in a graph G. A set S of edges is a v–w edge-separating set if v and w lie in different components of G − S: that is, if every v–w path contains an edge of S. The minimum cardinality of a v–w edge-separating set is the v–w edge-connectivity and is denoted by λ(v, w).
6. F. T. Boesch and S. Chen, A generalization of line connectivity and optimally invulnerable graphs, SIAM J. Appl. Math. 34 (1978), 657–665. 7. S. M. Boyles and G. Exoo, A counterexample on a conjecture on paths of bounded lengths, J. Graph Theory 6 (1982), 205–209. 8. G. Chartrand, A graph theoretic approach to a communications problem, SIAM J. Appl. Math. 14 (1996), 778–781. 9. G. Chartrand and F. Harary, Graphs with prescribed connectivities, Theory of Graphs, Proceedings of the Colloquium Held at Tihany, Hungary, Akadémiai Kaidó, 1968.
A graph G is uniformly k-connected if κ(G) = κ(G) = k. A graph G with connectivity k is critically k-connected if κ(G − v) < k for each vertex v, and is minimally k-connected if κ(G−e) < k for each edge e. Some necessary conditions for a graph to be uniformly k-connected were given by Beineke, Oellermann and Pippert . 2 Every uniformly k-connected graph is minimally k-connected if k ≥ 1, and is critically k-connected if k ≥ 2. These conditions are not sufficient, as there are graphs that are both minimally and critically k-connected, but not uniformly k-connected.