Results 31 to 40 of about 34,352 (308)

Diameter-invariant graphs [PDF]

Mathematica Bohemica, 2005
Summary: The diameter of a graph \(G\) is the maximal distance between two vertices of~\(G\). A graph \(G\) is said to be diameter-edge-invariant, if \(d(G-e)=d(G)\) for all its edges, diameter-vertex-invariant, if \(d(G-v)=d(G)\) for all its vertices and diameter-adding-invariant if \(d(G+e)=d(e)\) for all edges of the complement of the edge set of ...
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Minor-monotone crossing number [PDF]

Discrete Mathematics & Theoretical Computer Science, 2005
The minor crossing number of a graph $G$, $rmmcr(G)$, is defined as the minimum crossing number of all graphs that contain $G$ as a minor. We present some basic properties of this new minor-monotone graph invariant.
Drago Bokal, Gašper Fijavž, Bojan Mohar   +2 more
doaj   +1 more source

Does Invariant Graph Learning via Environment Augmentation Learn Invariance? [PDF]

, 2023
Invariant graph representation learning aims to learn the invariance among data from different environments for out-of-distribution generalization on graphs.
Chen, Yongqiang, Xie, Binghui, Bian, Yatao, Cheng, James, Zhou, Kaiwen, Han, Bo   +5 more
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Homomorphisms and polynomial invariants of graphs

European Journal of Combinatorics, 2007
Junta de Andalucía P06-FQM ...
Delia Garijo, Jaroslav Nesetril, M. P. Revuelta   +2 more
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Invariants of Graph Drawings in the Plane [PDF]

Arnold Mathematical Journal, 2020
48 pages, many figures.
openaire   +3 more sources

On Euler-Sombor index of benzenoids and phenylenes [PDF]

Kragujevac Journal of Science
The Euler-Sombor index of a graph, EU(G), is a recently introduced vertex-degree based topological index. It is derived from the geometric consideration of a graph.
Redžepović Izudin, Muminović Lejla
doaj   +1 more source

On a Minor-Monotone Graph Invariant

Journal of Combinatorial Theory, Series B, 1995
Let \(G= (V, E)\) be a finite graph and \(d\in N\). A function \(\phi: V\to R^d\) is called a valid representation of \(G\) if for any halfspace \(H\) of \(R^d\) the set \(\phi^{- 1}(H)\) is nonempty and induces a connected subgraph of \(G\). Then \(\lambda(G)\) is defined as the largest \(d\) for which a valid representation \(\phi: V\to R^d\) exists.
H. van der Holst, M. Laurent (Monique), A. Schrijver (Lex)   +2 more
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Minimal invariant sets in a vertex-weighted graph [PDF]

, 2006
A weighting of vertices of a graph is admissible if there exists an edge weighting such that the weight of each vertex equals the sum of weights of its incident edges.
Marina Moscarini, Francesco Mario Malvestuto, Malvestuto, Francesco M., MEZZINI, MAURO, MALVESTUTO, Francesco Mario, MOSCARINI, Marina   +5 more
core   +1 more source

Invariance, Quasi-Invariance, and Unimodularity for Random Graphs [PDF]

Journal of Mathematical Sciences, 2016
We interpret the probabilistic notion of unimodularity for measures on the space of rooted locally finite connected graphs in terms of the theory of measured equivalence relations. It turns out that the right framework for this consists in considering quasi-invariant (rather than just invariant) measures with respect to the root moving equivalence ...
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From the Ising and Potts Models to the General Graph Homomorphism Polynomial [PDF]

, 2016
A number of classical models in statistical physics, such as the Ising model, Potts model, and lattice gas, can be formulated in terms of the generating function for weighted versions of homo-morphisms from G to some graph H.
Klas Markström, Markström, Klas,
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