Results 21 to 30 of about 6,072 (265)

Vertex colouring edge partitions

Journal of Combinatorial Theory, Series B, 2005
Suppose that the edges of a graph are assigned labels from a \(k\)-set, or equivilently, the edges are partitioned into \(k\) parts. Each vertex \(v\) has an associated multiset \(X_v\) consisting of the labels on its incident edges. The partition is a (proper) vertex coloring if for every edge \(uv\), \(X_u \neq X_v\).
Louigi Addario-Berry, Robert E. L. Aldred, Ketan Dalal, Bruce A. Reed   +3 more
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Topological vertex/anti-vertex and supergroup gauge theory

Journal of High Energy Physics, 2020
We propose a new vertex formalism, called anti-refined topological vertex (anti-vertex for short), to compute the generalized topological string amplitude, which gives rise to the supergroup gauge theory partition function.
Taro Kimura, Yuji Sugimoto
doaj   +1 more source

Topological vertex for 6d SCFTs with ℤ2-twist

Journal of High Energy Physics, 2021
We compute the partition function for 6d N $$ \mathcal{N} $$ = 1 SO(2N) gauge theories compactified on a circle with ℤ2 outer automorphism twist. We perform the computation based on 5-brane webs with two O5-planes using topological vertex with two O5 ...
Hee-Cheol Kim, Minsung Kim, Sung-Soo Kim
doaj   +1 more source

THE PARTITION DIMENSION AND $k$-DOMINATION NUMBER OF TWO SPECIFIC GRAPHS [PDF]

Journal of Algebraic Systems
For an ordered $k$-partition $\Omega = \{S_1, S_2, ..., S_k\}$ of vertex set of a connected graph $G$ and a vertex $v$ of $G$, the representation of $v$ with respect to $\Omega$ is defined as the $k$-tuple $r(v |\Omega) = (d(v, S_1), d(v, S_2), ..., d(v,
Ali Zafari, Saeid Alikhani
doaj   +1 more source

Instanton counting and O-vertex

Journal of High Energy Physics, 2021
We present closed-form expressions of unrefined instanton partition functions for gauge groups of type BCD as sums over Young diagrams. For SO(n) gauge groups, we provide a fivebrane web picture of our formula based on the vertex-operator formalism of ...
Satoshi Nawata, Rui-Dong Zhu
doaj   +1 more source

Tree partitioning via vertex deletion

Electronic Notes in Discrete Mathematics, 2001
Abstract Motivated by tree partitioning problems, we introduce the notion of i-divider of a tree, t -dividers generalize concepts well-known in literature, such as centroids and separators, that are the backbone of tree decomposition algorithms based on vertex deletion.
FINOCCHI, Irene, PETRESCHI, Rossella
openaire   +3 more sources

On the Locating Chromatic Number of Certain Barbell Graphs

International Journal of Mathematics and Mathematical Sciences, 2018
The locating chromatic number of a graph G is defined as the cardinality of a minimum resolving partition of the vertex set V(G) such that all vertices have distinct coordinates with respect to this partition and every two adjacent vertices in G are not ...
Asmiati, I. Ketut Sadha Gunce Yana, Lyra Yulianti   +2 more
doaj   +1 more source

Vertex Set Partitions Preserving Conservativeness

Journal of Combinatorial Theory, Series B, 2000
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Alexander A. Ageev, Alexandr V. Kostochka   +1 more
openaire   +1 more source

THE PARTITION DIMENSION OF CYCLE BOOKS GRAPH B_(m,n) WITH A COMMON PATH P_2

Barekeng
Suppose  is a connected graph with  elements of a set of vertices  denoted by  and  a subset of . The distance between  and  is the shortest distance  to every vertex  in . Let  be a partition of , where each subset  belongs to .
Jaya Santoso, Darmaji Darmaji
doaj   +1 more source

A Note on Non-Dominating Set Partitions in Graphs

Discussiones Mathematicae Graph Theory, 2016
A set S of vertices of a graph G is a dominating set if every vertex not in S is adjacent to a vertex of S and is a total dominating set if every vertex of G is adjacent to a vertex of S.
Desormeaux Wyatt J., Haynes Teresa W., Henning Michael A.   +2 more
doaj   +1 more source