Graph theory can be used to model communities in the network, such as social media or contact tracing for illnesses and other outbreaks. Graph theory is used to model the internet where each web page is a node, and the hyperlinks between pages are the edges of the graph model. Graph theor...
Every k-connected graph G withδ(G)≥⌊3k2⌋+2 has an edgexy such thatG−{x,y} is stillk-connected. In the same paper, Fujita and Kawarabayashi posed the following conjecture. Conjecture 1.3 [3] For all positive integers k,m, there is a (least) non-negative integer fk(m)...
Although not all the classes of finite connected‐homomorphism‐homogeneous graphs are completely characterised, we may still obtain the final hierarchy picture for these classes.doi:10.1002/jgt.21788LockettDeborah C.Journal of Graph Theory
A lower bound on the independence number of a graph in terms of degrees Discuss. Math. Graph Theory, 26 (2006), pp. 431-437 CrossrefGoogle Scholar [7] J. Håstad, Clique is hard to approximate within n1−ϵ, in: Proceedings of 37th Annual Symposium on Foundations of Computer Scie...
Intuitively, this is a connected graph because you can always go from one vertex to another using their connections. The idea of the above definition is to show this by using permutations. The natural permutation to be chosen in this example is $\pi(1) = 2$, $\pi(2) = 3$ and $\...
Again we need some basic graph theory. Let us, for a while, admit nonsimple graphs as well, that is, graphs that can have loops and parallel edges. Such a graph G is connected if there is a path bet…
Also I'm in the computer sciences so it would be great to know if I have made any mistakes in expressing the maths involved in this question. Edit: Might have answered my own question, can I just write vin={e∣et=v}vin={e∣et=v}? elementary-set-theory graph-theory notatio...
View in ScopusGoogle Scholar [2] W. Mader Connectivity and edge-connectivity in finite graphs B. Bollobás (Ed.), Surveys in Combinatorics, Cambridge University Press, London (1979), pp. 66-95 Google Scholar [3] D.W. Matula Ramsey theory for graph connectivity J. Graph Theory, 7 (1983)...
In this century psychologically-relevantneurosciencehas steadily moved from a focus on the function of particular regions of interest (ROIs) to the role of distributed brainnetworks.Petersen and Sporns (2015)use terms from graph theory and network science to define a network as “… a set of ...
Win proved a very famous conclusion that states the graph G with connectivity κ(G), independence number α(G) and α(G)≤κ(G)+k−1(k≥2) contains a spanning k-ended tree. This means that there exists a spanning tree with at most k leaves. In this pap