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Local Partition Dimension of Grid Graph and Its Application to the Coordinates of Potential Disaster Areas in Jember Regency

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, Reni Umilasari, Nanang Saiful Rizal   +2 more
doaj   +1 more source

Topological minors of cover graphs and dimension [PDF]

, 2016
We show that posets of bounded height whose cover graphs exclude a fixed graph as a topological minor have bounded dimension. This result was already proven by Walczak.
Dujmović, Felsner, Felsner, Felsner, Füredi, Grohe, Joret, Kelly, Kierstead, Lasoń, Micek, Robertson, Streib, Trotter, Trotter, Trotter, Walczak   +16 more
core   +1 more source

Scrambling in Yang-Mills

Journal of High Energy Physics, 2021
Acting on operators with a bare dimension ∆ ∼ N 2 the dilatation operator of U(N) N $$ \mathcal{N} $$ = 4 super Yang-Mills theory defines a 2-local Hamiltonian acting on a graph.
Robert de Mello Koch, Eunice Gandote, Augustine Larweh Mahu   +2 more
doaj   +1 more source

Spectral Dimension Reduction of Complex Dynamical Networks [PDF]

Physical Review X, 2018
Dynamical networks are powerful tools for modeling a broad range of complex systems, including financial markets, brains, and ecosystems. They encode how the basic elements (nodes) of these systems interact altogether (via links) and evolve (nodes ...
Edward Laurence, N. Doyon, Louis J. Dub'e, Patrick Desrosiers   +3 more
semanticscholar   +1 more source

A central local metric dimension on acyclic and grid graph

AIMS Mathematics, 2023
The local metric dimension is one of many topics in graph theory with several applications. One of its applications is a new model for assigning codes to customers in delivery services. Let $ G $ be a connected graph and $ V(G) $ be a vertex set of $ G $.
Yuni Listiana, Liliek Susilowati, Slamin Slamin, Fadekemi Janet Osaye   +3 more
doaj   +1 more source

Search for the end of a path in the d-dimensional grid and in other graphs [PDF]

, 2015
We consider the worst-case query complexity of some variants of certain \cl{PPAD}-complete search problems. Suppose we are given a graph $G$ and a vertex $s \in V(G)$.
Gerbner, Dániel, Keszegh, Balázs, Pálvölgyi, Dömötör, Rote, Günter, Wiener, Gábor   +4 more
core   +2 more sources

The Application of Fault-Tolerant Partition Resolvability in Cycle-Related Graphs

Applied Sciences, 2022
The concept of metric-related parameters permeates all of graph theory and plays an important role in diverse networks, such as social networks, computer networks, biological networks and neural networks.
Kamran Azhar, Sohail Zafar, Agha Kashif, Amer Aljaedi, Umar Albalawi   +4 more
doaj   +1 more source

A Central Local Metric Dimension of Generalized Fan Graph, Generalized Broken Fan Graph, and Cm ⊙ K¯m [PDF]

E3S Web of Conferences
The central local metric dimension is a new variation of local metric dimension that introduced in 2023. The central local metric dimension is a new concept that enriches research studies in graph theory, especially in the field of metric dimension. This
Listiana Yuni, Susilowati Liliek, Slamin
doaj   +1 more source

A simpler proof for the dimension of the graph of the classical Weierstrass function

, 2017
. Let W λ,b (x) = (cid:2) ∞ n = 0 λ n g(b n x) where b ≥ 2 is an integer and g(u) = cos ( 2 πu) (classical Weierstrass function). Building on work by Ledrappier (In Symbolic Dynamics and Its Applications (1992) 285–293), Bara´nski, Bárány and Romanowska (
G. Keller
semanticscholar   +1 more source