Dimensi Partisi Pada Graf

Khairiah, Annisatul; Noviani, Evi; Fran, Fransiskus

doi:10.26418/bbimst.v9i1.38818

Cited by 3 publications

(2 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Selanjutnya menentukan jarak seluruh simpul terhadap setiap kelas partisi untuk mendapatkan representasi. Representasi yang memiliki vektor koordinat berbeda dan memiliki jumlah kardinalitas minimum merupakan dimensi partisi dari graf [5].…”

Section: Pendahuluanunclassified

Dimensi Partisi pada Graf Hasil Operasi Korona Tingkat-k

Amalia,

Ummi Nur Yatun Hasanah,

Faisol

et al. 2024

Contemp. Math. App

View full text Add to dashboard Cite

Graph theory is one of the subjects in Discrete Mathematics that have long been known and are widely applied in various fields. The topics that are often discussed in graph theory include labeling, coloring, chromatic numbers, metric dimensions, and partition dimensions. Partition dimensions are obtained by grouping all the vertices on the graph into a number of partition classes, then determine the distance of all vertices to each partition class to get a representation. Partition class which representations have different coordinate vectors is called resolving partition. The minimum cardinality of resolving partition is called partition dimensions of the graph. The purpose of this study is to determine the partition dimensions of level corona operation graphs which are GʘkPm, GʘkCm and GʘkKm, where G, Pm, Cm and Km are connected non trivial graph, path graph, circle graph and complete graph respectively, and any integer k≥1.

show abstract

Section: Pendahuluanunclassified

Dimensi Partisi pada Graf Hasil Operasi Korona Tingkat-k

Amalia,

Ummi Nur Yatun Hasanah,

Faisol

et al. 2024

Contemp. Math. App

View full text Add to dashboard Cite

show abstract

“…The partition dimension is the result of the development of the metric dimension. As an explanation, a set known as a locating set is often known as a resolving set (Fransiskus Fran, 2020). Furthermore, the concept of a discriminating partition is similar to the resolving set of the graph.…”

Section: A Introductionmentioning

confidence: 99%

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

Saifudin,

Umilasari,

Rizal

2023

JTAM

View full text Add to dashboard Cite

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 vertices 𝑣 to which is Π denoted by 𝑟(𝑣| Π). One of the conditions that must be met for 𝑟(𝑣| Π) is discussed. The minimum value of k so that there is a local distinguishing partition from V (G) is the local partition dimension of G or it can can be said that the distance of each neighbor is different. The local partition dimension of a graph G is denoted 〖pd〗_l (G). In this study, we used an axiomatic deductive methods and pattern recognition. In order to construct the discriminating set on the metric dimension (dim) and the discriminating partition on the partition dimension (pd), the pattern detection method looks for patterns in which the coordinate values are minimum and different. By all observations, the local partition dimensions of P_n×P_m Grid graph has two condition about the results of resolving partition. The Result of local partition dimension of a Grid graph 〖〖pd〗_l (P〗_n×P_m)=2, where n≥2 dan m≥2. In addition, it will decide how to convert the coordinates of areas in the Jember district that are prone to flooding and landslides into metric dimensions. It was about Coordinates of Flood and Landslide Disaster Locations in Jember Regency. The number of local and minimal partition sets generated for flood-prone areas in Jember Regency is 〖pd〗_l (G_Jember)=3.

show abstract

Partition Dimension of Generalized Hexagonal Cellular Networks and Its Application

Bhatti,

Jamil,

Azeem

et al. 2024

IEEE Access

View full text Add to dashboard Cite

The notion of partition dimension was initially introduced in the field of graph theory, primarily to examine distances between vertices. The local partition dimension extends this idea by incorporating specific conditions into how vertices are represented. In graph theory, it is customary to represent the partition dimension of a graph as pd(G). Network localization, on the other hand, is the process of precisely determining the position of nodes within a network concerning a selected subset of nodes, called the locating set. The smallest size of its locating set is used to represent the locating number of a network. The generalized hexagonal cellular network provides an innovative framework for network planning and analysis. In our study, we investigate the partition dimension of a generalized hexagonal cellular network and provide a rigorous proof of its exact partition dimension. Hence, our approach ensures the distinct recognition of each node within a generalized hexagonal cellular network. Additionally, we explore the utilization of the metric dimension in flood relief camping by the National Disaster Management Authority (NDMA) Pakistan during floods in 2022. NDMA established relief camps and relief centers with unique codes to rescue humans and animals.

show abstract

Dimensi Partisi Pada Graf

Cited by 3 publications

References 0 publications

Dimensi Partisi pada Graf Hasil Operasi Korona Tingkat-k

Dimensi Partisi pada Graf Hasil Operasi Korona Tingkat-k

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

Partition Dimension of Generalized Hexagonal Cellular Networks and Its Application

Contact Info

Product

Resources

About