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DONALDSON–THOMAS INVARIANTS OF LOCAL ELLIPTIC SURFACES VIA THE TOPOLOGICAL VERTEX
Forum of Mathematics, Sigma, 2019 We compute the Donaldson–Thomas invariants of a local elliptic surface with section. We introduce a new computational technique which is a mixture of motivic and toric methods. This allows us to write the partition function for the invariants in terms of
JIM BRYAN, MARTIJN KOOL
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One-Dimensional Vertex Models Associated with a Class of Yangian Invariant Haldane-Shastry Like Spin Chains [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2010 We define a class of Y(sl_{(m|n)}) Yangian invariant Haldane-Shastry (HS) like spin chains, by assuming that their partition functions can be written in a particular form in terms of the super Schur polynomials.
Kazuhiro Hikami +2 more
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A social network graph partitioning algorithm based on double deep Q-Network [PDF]
Scientific ReportsWith the rapid expansion of social networks, efficiently mining and analyzing massive graph data has become a fundamental challenge in social network research. Graph partitioning plays a pivotal role in enhancing the performance of such analyses. However,
Jie Cao +4 more
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Topological structures induced by chromatic partitioning of vertex set of graphic [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 This paper presents a method of constructing topologies on vertex set of a graph G induced by chromatic partition of vertex set of the graph. It introduces colour lower approximation and colour upper approximation of vertex induced subgraphs and ...
K. Lalithambigai, P. Gnanachandra
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Opuscula Mathematica, 2023 A coalition in a graph \(G = (V, E)\) consists of two disjoint sets \(V_1\) and \(V_2\) of vertices, such that neither \(V_1\) nor \(V_2\) is a dominating set, but the union \(V_1 \cup V_2\) is a dominating set of \(G\). A coalition partition in a graph \
Teresa W. Haynes +4 more
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The partition dimension of the vertex amalgamation of some cycles
Heliyon, 2022 Let G=(V(G),E(G)) be a connected, finite, simple, and undirected graph. The distance between two vertices u,w∈V(G), denoted by d(u,w), is the shortest length of (u,w)-path in G.
Hasmawati +4 more
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More on topological vertex formalism for 5-brane webs with O5-plane
Journal of High Energy Physics, 2021 We propose a concrete form of a vertex function, which we call O-vertex, for the intersection between an O5-plane and a 5-brane in the topological vertex formalism, as an extension of the work of [1].
Hirotaka Hayashi, Rui-Dong Zhu
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On the Bounded Partition Dimension of Some Generalised Graph Structures
Journal of Mathematics, 2022 Consider λ to be a connected graph with a vertex set Vλ that may be partitioned into any partition set S. If each vertex in λ has a separate representation with regard to S and is an ordered k partition, then the set with S is a resolving partition of λ..
Wajdi Alghamdi, Muhammad Ahsan Asim
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Computing the partition dimension of certain families of Toeplitz graph
Frontiers in Computational Neuroscience, 2022 Let G = (V(G), E(G)) be a graph with no loops, numerous edges, and only one component, which is made up of the vertex set V(G) and the edge set E(G). The distance d(u, v) between two vertices u, v that belong to the vertex set of H is the shortest path ...
Ricai Luo +5 more
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Partition Dimension of Generalized Petersen Graph
Complexity, 2021 Let G=VG,EG be the connected graph. For any vertex i∈VG and a subset B⊆VG, the distance between i and B is di;B=mindi,j|j∈B. The ordered k-partition of VG is Π=B1,B2,…,Bk. The representation of vertex i with respect to Π is the k-vector, that is, ri|Π=di,
Hassan Raza +3 more
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