Koch [31] presented an efficient algorithm called c-cliques based on the MCES (or maximum overlapping set (MOS)) concept that identifies cliques by pruning a given graph on the basis of certain constraints (c-edges and d-edges) before using the Bron Kerbosch algorithm to find the MCS.
The bandlimited graph signal f can be reconstructed from its downsampling set S by IGDR, for a given graph cut-off frequency w, the reconstructed error bound of IGDR is begin{array}rcl@ {eta^{k + 1}} < {left| {{{mathcal{F}}^{- 1}}{P_{w}}{mathcal{F}}left {I - {P_{T}}} right)left {I - {P_{d}}{P_{T}}} right)} right|^{k}} cdot {eta^{0}} end{array} (14).
This paper considers the problem of augmenting a given graph by a cheapest possible set of additional edges in order to make the graph edge-biconnected.
We enumerate all sub-graphs that meet the requirements of a given graph by way of reducing the searching space.
The double graph of a given graph G, denoted by G ⊛, is constructed by making two copies of G (including the initial edge set of each), denoted by G 1 and G 2, and adding edges u 1 v 2 and u 2 v 1 for every edge uv of G. From the definition of composition, we conclude that G ⊛ ≅ G [ K 2 ] for any connected graph G. Therefore the following corollary can be easily obtained.
More precisely, the graph edit distance measure is based on applying graph transformations, i.e, a sequence of weighted graph edit operations that transform a given graph into another graph by producing minimal edit costs [32].
By adding additional control points, the given graph examples show that the trigonometric polynomial curves are nearer their control polygons than the Bézier curves for the same parametric variable and the same degree.
Take the given graph and add edges by duplicating existing ones, until you arrive at a graph that is connected and has all even degree vertices.
Our focus is on understanding which properties shared by the individual input graphs will transfer to the output graph returned by a given aggregation rule.
When possible transformations of a given molecular graph represented by a set of molecular bond paths are considered, it can be shown that 'the ellipticity of the bond which is to be broken increases dramatically and becomes infinite at the geometry of the bifurcation point' so that 'a structure possessing a bond with an unusually large ellipticity is potentially unstable' [37].
