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The metric dimension of circulant graphs [PDF]

Opuscula Mathematica
A pair of vertices \(x\) and \(y\) in a graph \(G\) are said to be resolved by a vertex \(w\) if the distance from \(x\) to \(w\) is not equal to the distance from \(y\) to \(w\).
Tapendra BC, Shonda Dueck
doaj   +1 more source

Post‐surgery level of circulating DNA in stage III colon cancer patients: Impact on the reliability of minimal residual disease detection

International Journal of Cancer, Volume 158, Issue 10, Page 2771-2783, 15 May 2026.
What's New? Circulating nuclear DNA (cir‐nDNA)‐based assessment of minimal residual disease (MRD) offers powerful post‐surgery prognostic insight for stage III colon cancer (CC). Sparse knowledge of post‐surgical variations and origins in cir‐nDNA, however, has limited its clinical application.
Andrei Kudriavtsev, Saidi Daoud, Catalina Isabel Cofre Muñoz, Alexia Mirandola, Ekaterina Pisareva, Javier Gonzalo Ruiz, Marco Macagno, Nadia Saoudi Gonzalez, Evelyne Crapez, Marc Ychou, Ramon Salazar Soler, Elisabetta Fenocchio, Paula X. Fernandez Calotti, Thibault Mazard, Cristina Santos Vivas, Elena Elez, Federica Di Nicolantonio, Alain R. Thierry   +17 more
wiley   +1 more source

On the page-number of a circulant graph

AKCE International Journal of Graphs and Combinatorics
The page-number of a graph G, denoted by p(G), is the minimum k such that G has an embedding in a k-book. The circulant graph C(m, n) is such a graph that its vertex set is [Formula: see text] and edge set is [Formula: see text], where m, n are positive ...
Xiaoyuan Dong, Dengju Ma
doaj   +1 more source

Block circulant graphs and the graphs of critical pairs of crowns

Electronic Journal of Graph Theory and Applications, 2019
In this paper, we provide a natural bijection between a special family of block circulant graphs and the graphs of critical pairs of the posets known as generalized crowns.
Rebecca E. Garcia, Pamela E. Harris, Bethany Kubik, Shannon Talbott   +3 more
doaj   +1 more source

Accelerating Conjugate Gradient Solvers for Homogenization Problems With Unitary Neural Operators

International Journal for Numerical Methods in Engineering, Volume 127, Issue 5, 15 March 2026.
ABSTRACT Rapid and reliable solvers for parametric partial differential equations (PDEs) are needed in many scientific and engineering disciplines. For example, there is a growing demand for composites and architected materials with heterogeneous microstructures.
Julius Herb, Felix Fritzen
wiley   +1 more source

Definition and Computation of Tensor‐Based Generalized Function Composition

Numerical Linear Algebra with Applications, Volume 33, Issue 1, February 2026.
ABSTRACT Functions are fundamental to mathematics as they offer a structured and analytical framework to express relations between variables. While scalar and matrix‐based functions are well‐established, higher‐order tensor‐based functions have not been as extensively explored.
Remy Boyer
wiley   +1 more source

Circulant graph imbeddings

Journal of Combinatorial Theory, Series B, 1980
AbstractAn algebraic characterization is given for those Cayley graphs for cyclic groups in which the neighborhood of any vertex is a cycle. A triangular imbedding is obtained for each such graph, either in the sphere, the torus, or the Klein bottle.
openaire   +2 more sources

Algebraic Connectivity Maximizing Regular Graphs: Special Case Analysis and Depth‐First Search

Concurrency and Computation: Practice and Experience, Volume 37, Issue 27-28, 25 December 2025.
ABSTRACT The algebraic connectivity is an indicator of how well connected a graph is. It also characterizes the convergence speed of some dynamic processes over networks. In this paper, taking into account that homogeneous networks are modeled as regular graphs, we tackle the following problem: given a pair (n,k)$$ \left(n,k\right) $$ of positive ...
Masashi Kurahashi, Najd Salaani, Tsuyoshi Migita, Norikazu Takahashi   +3 more
wiley   +1 more source

The metric dimension of circulant graphs and their Cartesian products [PDF]

Opuscula Mathematica, 2017
Let \(G=(V,E)\) be a connected graph (or hypergraph) and let \(d(x,y)\) denote the distance between vertices \(x,y\in V(G)\). A subset \(W\subseteq V(G)\) is called a resolving set for \(G\) if for every pair of distinct vertices \(x,y\in V(G)\), there ...
Kevin Chau, Shonda Gosselin
doaj   +1 more source

Enumeration of E ( s 2 )‐Optimal and Minimax‐Optimal Supersaturated Designs With 12 Rows, 11 q Columns and s max = 4

Journal of Combinatorial Designs, Volume 33, Issue 10, Page 379-387, October 2025.
ABSTRACT The E ( s 2 )‐optimal and minimax‐optimal supersaturated designs (SSDs) with 12 rows, 11 q columns, and s max = 4 are enumerated in a computer search: there are, respectively, 34, 146, 0, 3, and 1 such designs for q = 2 , 3 , 4 , 5, and 6. Cheng and Tang proved that for q > 6, there are no such SSDs.
Luis B. Morales
wiley   +1 more source