Graphs whose mixed metric dimension is equal to their order

Ghalavand, Ali; Klavžar, Sandi; Tavakoli, Mostafa

doi:10.1007/s40314-023-02351-5

Cited by 1 publication

(3 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In general, 2p − 2 is the minimal cardinality and 2p − 1 is the maximal cardinality for all prime numbers. So, by relation (2) and Theorem 1, we have…”

Section: Stream Values Of Lfmd For Certain Families Of Toeplitz Graphsmentioning

confidence: 87%

“…Since the minimum and maximum cardinalities of the resolving sets are ℘ 2 and ℘ − 2, respectively, by relation (2) and Theorem 1, we have:…”

Section: Stream Values Of Lfmd For Certain Families Of Toeplitz Graphsmentioning

confidence: 98%

“…The need to understand the structural qualities of graphs in terms of the labeling of their vertices and the connections between their nodes led to the development of the idea of metric dimension. Metric dimension has practical implications in network design, graph theory, and optimization [1][2][3].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On Sharp Bounds of Local Fractional Metric Dimension for Certain Symmetrical Algebraic Structure Graphs

Alali,

Ali,

Adnan

et al. 2023

Symmetry

View full text Add to dashboard Cite

The smallest set of vertices needed to differentiate or categorize every other vertex in a graph is referred to as the graph’s metric dimension. Finding the class of graphs for a particular given metric dimension is an NP-hard problem. This concept has applications in many different domains, including graph theory, network architecture, and facility location problems. A graph G with order n is known as a Toeplitz graph over the subset S of consecutive collections of integers from one to n, and two vertices will be adjacent to each other if their absolute difference is a member of S. A graph G(Zn) is called a zero-divisor graph over the zero divisors of a commutative ring Zn, in which two vertices will be adjacent to each other if their product will leave the remainder zero under modulo n. Since the local fractional metric dimension problem is NP-hard, it is computationally difficult to identify an optimal solution or to precisely determine the minimal size of a local resolving set; in the worst case, the process takes exponential time. Different upper bound sequences of local fractional metric dimension are suggested in this article, along with a comparison analysis for certain families of Toeplitz and zero-divisor graphs. Furthermore, we note that the analyzed local fractional metric dimension upper bounds fall into three metric families: constant, limited, and unbounded.

show abstract

“…In general, 2p − 2 is the minimal cardinality and 2p − 1 is the maximal cardinality for all prime numbers. So, by relation (2) and Theorem 1, we have…”

Section: Stream Values Of Lfmd For Certain Families Of Toeplitz Graphsmentioning

confidence: 87%

“…Since the minimum and maximum cardinalities of the resolving sets are ℘ 2 and ℘ − 2, respectively, by relation (2) and Theorem 1, we have:…”

Section: Stream Values Of Lfmd For Certain Families Of Toeplitz Graphsmentioning

confidence: 98%

See 1 more Smart Citation

On Sharp Bounds of Local Fractional Metric Dimension for Certain Symmetrical Algebraic Structure Graphs

Alali,

Ali,

Adnan

et al. 2023

Symmetry

View full text Add to dashboard Cite

show abstract

Graphs whose mixed metric dimension is equal to their order

Cited by 1 publication

References 14 publications

On Sharp Bounds of Local Fractional Metric Dimension for Certain Symmetrical Algebraic Structure Graphs

On Sharp Bounds of Local Fractional Metric Dimension for Certain Symmetrical Algebraic Structure Graphs

Contact Info

Product

Resources

About