Results 1 to 10 of about 344,286 (183)
The edge partition dimension of graphs [PDF]
Discrete Mathematics Letters, 2023 Theedgemetric dimension wasintroduced in 2018 and since then, it has been extensively studied. In this paper, we present a different way to obtain resolving structures in graphs in order to gain more insight into the study of edge resolving sets andresolving partitions. We define the edge partition dimension of a connected graph and bound it for graphs
Dorota Kuziak +3 more
doaj +3 more sources
Computing the partition dimension of certain families of Toeplitz graph [PDF]
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
doaj +2 more sources
All graphs of order n ≥ 11 and diameter 2 with partition dimension n − 3 [PDF]
Heliyon, 2020 All graphs of order n with partition dimension 2, n−2, n−1, or n have been characterized. However, finding all graphs on n vertices with partition dimension other than these above numbers is still open.
Edy Tri Baskoro, Debi Oktia Haryeni
doaj +2 more sources
The partition dimension of the vertex amalgamation of some cycles [PDF]
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
doaj +2 more sources
On the strong partition dimension of graphs [PDF]
The Electronic Journal of Combinatorics, 2013 We present a different way to obtain generators of metric spaces having the property that the ``position'' of every element of the space is uniquely determined by the distances from the elements of the generators.
Yero, Ismael Gonzalez
core +4 more sources
One-loop tests of supersymmetric gauge theories on spheres [PDF]
Journal of High Energy Physics, 2017 We show that a recently conjectured form for perturbative supersymmetric partition functions on spheres of general dimension d is consistent with the flat space limit of 6-dimensional N $$ \mathcal{N} $$ = 1 super Yang-Mills.
Joseph A. Minahan, Usman Naseer
doaj +4 more sources
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
doaj +2 more sources
The most irrational rational theories [PDF]
Journal of High Energy Physics, 2019 We propose a two-parameter family of modular invariant partition functions of two-dimensional conformal field theories (CFTs) holographically dual to pure three-dimensional gravity in anti de Sitter space.
Nathan Benjamin +3 more
doaj +4 more sources
JTAM (Jurnal Teori dan Aplikasi Matematika), 2023 Partition dimension was introduced as a part of interesting topic in graph theory. It was focus to observe about distance. The local partition dimension is an expansion of the partition dimension by adding certain conditions to the representation of the ...
Ilham Saifudin +2 more
doaj +1 more source
The Bridge Graphs Partition Dimension
Journal of Physics: Conference Series, 2021 Abstract Finding the partition dimension of graph is still an open problem in the graph theory. Therefore, several researchers investigate the problem in several operations of the graph. For example, the partition dimension of corona product, cartesian product, subdivision operation has been published by several researchers. Let G1, G2
A Amrullah +4 more
openaire +1 more source