Search results

...known as the '''connectivity index''', of a [[Graph (discrete mathematics)|graph]] is the sum of bond contributions <math>1/(d_i d_j)^{1/2}</math> where <ma This [[graph invariant]] was introduced by [[Milan Randić]] in 1975.<ref>{{citation|firs ...

In [[algebraic topology]], '''homological connectivity''' is a property describing a [[topological space]] based on its [[homology ...graph having a single connected component, which is equivalent to [[graph connectivity]]. It is similar to the notion of a [[connected space]]. ...

{{Short description|Topological space arising from a usual graph}} ...pological space]] which arises from a usual [[graph (discrete mathematics)|graph]] <math>G = (E, V)</math> by replacing vertices by points and each edge <ma ...

{{Graph connectivity sidebar}} ...math|''n''}} equal the number of [[Vertex (graph theory)|vertices]] of the graph. ...

{{Short description|Graph-theoretic connectivity parameter}} {{infobox graph ...

{{Short description|Binary operation in graph theory}} ...is a good [[Expander graph|expander]], then the expansion of the resulting graph is only slightly worse than the expansion of <math>G</math>. ...

...e vertices of the graph, then a convex <math>X</math>-embedding embeds the graph in such a way that every vertex either belongs to <math>X</math> or is plac ...his way will be a convex polygon, resulting in a [[convex drawing]] of the graph.{{r|tutte}} ...

...d to the [[homological connectivity]] of the [[independence complex]] of a graph, which is the smallest index ''k'' such that all reduced homological groups ...[independence complex]] of ''G'', has a high [[Connectivity (graph theory)|connectivity]]; NON wants to prove the opposite. ...

...weight, so that the added edges make the graph into a [[strongly connected graph]]. The strong connectivity augmentation problem was formulated by {{harvs|last1=Eswaran|first1=Kapali| ...

{{Short description|Graph with 24 vertices and 36 edges}} {{infobox graph ...

{{Short description|Semi-symmetric cubic graph with 110 vertices and 165 edges}} {{Infobox graph ...

[[File:Grinberg 5CEC Nonhamiltonian graph.svg|thumb|A graph that can be proven non-Hamiltonian using Grinberg's theorem]] ...xample]]s to [[Tait's conjecture]] that [[cubic graph|cubic]] [[polyhedral graph]]s are Hamiltonian. ...

{{short description|Deals with partial connectivity for a discrete space}} ...bda-connectedness ''' (or '''&lambda;-connectedness''') deals with partial connectivity for a [[discrete space]]. ...

{{Short description|Abstraction of graph shortest cycles}} ...cle in a graph, the edge connectivity of a graph, Hall sets in [[bipartite graph]]s, even sets in families of sets, and general position of point sets. It i ...

...ph connectivity]]. The input to the problem is a [[regular graph|2-regular graph]], forming either a single connected <math>n</math>-vertex cycle or two dis | contribution = Parallel algorithms for geometric graph problems ...

...>, with <math>h(G)</math> defined to be the length of the longest cycle in graph <math>G</math>, the shortness exponent is defined as<ref name="gw">{{citati The shortness exponent of the [[polyhedral graph]]s is <math>\log_3 2\approx 0.631</math>. A construction based on [[kleetop ...

...ance-transitive]] [[graph (discrete mathematics)|graph]]s having [[degree (graph theory)|degree]] greater than 2.<ref>{{cite journal|last1=Cameron |first1=P [[Category:Algebraic graph theory]] ...

However, if we deal with a synthetic graph sequence <math>G_{N}</math>, or a network model that is well defined for ne ...422}}</ref> According to this definition, the [[Star (graph theory)|N-star graph]] <math>S_N</math>, for example, is not sparse. ...

...c data structure]] that maintains the [[minimum spanning tree]] (MST) of a graph whose edge weights are changing as a continuous function of time. ...structure considers the [[Duality (projective geometry)|dual]] view of the graph, and then [[divide and conquer paradigm|divides]] based on Frederickson's r ...

{{Short description|Partition of vertices of a directed graph}} ...a [[directed graph]] [[partition of a set|partition]] the vertices of the graph into subsets that are [[totally ordered]] by [[reachability]]. They form th ...