A Combinatorial Approach to the Computation of the Fractional Edge Dimension of Graphs

E. Yi recently introduced the fractional edge dimension of graphs. It has many applications in different areas of computer science such as in sensor networking, intelligent systems, optimization, and robot navigation. In this paper, the fractional edge dimension of vertex and edge transitive graphs is calculated. The class of hypercube graph Qn with an odd number of vertices n is discussed. We propose the combinatorial criterion for the calculation of the fractional edge dimension of a graph, and hence applied it to calculate the fractional edge dimension of the friendship graph Fk and the class of circulant graph Cn(1,2).

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On fault-tolerant partition dimension of graphs

Journal of Intelligent & Fuzzy Systems ◽

10.3233/jifs-201390 ◽

2021 ◽

Vol 40 (1) ◽

pp. 1129-1135

Author(s):

Kamran Azhar ◽

Sohail Zafar ◽

Agha Kashif ◽

Zohaib Zahid

Keyword(s):

Connected Graph ◽

Intelligent Systems ◽

Fault Tolerant ◽

Robot Navigation ◽

Natural Extension ◽

Resolving Set ◽

Minimum Cardinality ◽

Sensor Networking ◽

Partition Dimension

Fault-tolerant resolving partition is natural extension of resolving partitions which have many applications in different areas of computer sciences for example sensor networking, intelligent systems, optimization and robot navigation. For a nontrivial connected graph G (V (G) , E (G)), the partition representation of vertex v with respect to an ordered partition Π = {Si : 1 ≤ i ≤ k} of V (G) is the k-vector r ( v | Π ) = ( d ( v , S i ) ) i = 1 k , where, d (v, Si) = min {d (v, x) |x ∈ Si}, for i ∈ {1, 2, …, k}. A partition Π is said to be fault-tolerant partition resolving set of G if r (u|Π) and r (v|Π) differ by at least two places for all u ≠ v ∈ V (G). A fault-tolerant partition resolving set of minimum cardinality is called the fault-tolerant partition basis of G and its cardinality the fault-tolerant partition dimension of G denoted by P ( G ) . In this article, we will compute fault-tolerant partition dimension of families of tadpole and necklace graphs.

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On 2-metric resolvability in rotationally-symmetric graphs

Journal of Intelligent & Fuzzy Systems ◽

10.3233/jifs-210040 ◽

2021 ◽

pp. 1-9

Author(s):

Humera Bashir ◽

Zohaib Zahid ◽

Agha Kashif ◽

Sohail Zafar ◽

Jia-Bao Liu

Keyword(s):

Network Optimization ◽

Intelligent Systems ◽

Robot Navigation ◽

Data Transformation ◽

Metric Dimension ◽

Intelligent Networks ◽

Symmetric Graphs ◽

Symmetric Plane ◽

Rotationally Symmetric ◽

Sensor Networking

The 2-metric resolvability is an extension of metric resolvability in graphs having several applications in intelligent systems for example network optimization, robot navigation and sensor networking. Rotationally symmetric graphs are important in intelligent networks due to uniform rate of data transformation to all nodes. In this article, 2-metric dimension of rotationally symmetric plane graphs Rn, Sn and Tn is computed and found to be independent of the number of vertices.

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Bounds on the partition dimension of convex polytopes

Combinatorial Chemistry & High Throughput Screening ◽

10.2174/1386207323666201204144422 ◽

2020 ◽

Vol 23 ◽

Author(s):

Jia-Bao Liu ◽

Muhammad Faisal Nadeem ◽

Mohammad Azeem

Keyword(s):

Combinatorial Optimization ◽

Computer Science ◽

Facility Location ◽

Robot Navigation ◽

Convex Polytopes ◽

Pharmaceutical Chemistry ◽

Resolving Set ◽

Minimum Number ◽

Partition Dimension ◽

Np Problem

Aims and Objective: The idea of partition and resolving sets plays an important role in various areas of engineering, chemistry and computer science such as robot navigation, facility location, pharmaceutical chemistry, combinatorial optimization, networking, and mastermind game. Method: In a graph to obtain the exact location of a required vertex which is unique from all the vertices, several vertices are selected this is called resolving set and its generalization is called resolving partition, where selected vertices are in the form of subsets. Minimum number of partitions of the vertices into sets is called partition dimension. Results: It was proved that determining the partition dimension a graph is nondeterministic polynomial time (NP) problem. In this article, we find the partition dimension of convex polytopes and provide their bounds. Conclusion: The major contribution of this article is that, due to the complexity of computing the exact partition dimension we provides the bounds and show that all the graphs discussed in results have partition dimension either less or equals to 4, but it cannot been be greater than 4.

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Advances in Intelligent Systems, Computer Science and Digital Economics II

10.1007/978-3-030-80478-7 ◽

2021 ◽

Keyword(s):

Computer Science ◽

Intelligent Systems ◽

Digital Economics

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The Conference “Intelligent Systems and Computer Science”

Journal of Mathematical Sciences ◽

10.1007/s10958-010-9968-z ◽

2010 ◽

Vol 168 (1) ◽

pp. 1-1

Keyword(s):

Computer Science ◽

Intelligent Systems

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Failure Analysis in University and Computer Science Contexts With Data Mining

10.5753/wei.2020.11132 ◽

2020 ◽

Author(s):

Daniela De Souza Gomes ◽

Marcos Henrique Fonseca Ribeiro ◽

Giovanni Ventorim Comarela ◽

Gabriel Philippe Pereira

Keyword(s):

Data Mining ◽

Decision Making ◽

Failure Analysis ◽

Computer Science ◽

Educational Administration ◽

Intelligent Systems ◽

Data Set ◽

Data Mining Techniques ◽

Study Case ◽

Support Students

High failure rates are a worrying and relevant problem in Brazilian universities. From a data set of student transcripts, we performed a study case for both general and Computer Science contexts, in which Data Mining Techniques were used to find patterns concerning failures. The knowledge acquired can be used for better educational administration and also build intelligent systems to support students’ decision making.

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On Edge-Transitive Graphs of Square-Free Order

The Electronic Journal of Combinatorics ◽

10.37236/4573 ◽

2015 ◽

Vol 22 (3) ◽

Cited By ~ 3

Author(s):

Cai Heng Li ◽

Zai Ping Lu ◽

Gai Xia Wang

Keyword(s):

Automorphism Groups ◽

Edge Transitive ◽

Transitive Graphs ◽

Free Order

We study the class of edge-transitive graphs of square-free order and valency at most $k$. It is shown that, except for a few special families of graphs, only finitely many members in this class are basic (namely, not a normal multicover of another member). Using this result, we determine the automorphism groups of locally primitive arc-transitive graphs with square-free order.

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