Computing the Mixed Metric Dimension of a Generalized Petersen Graph P(n, 2)

The K -Size Edge Metric Dimension of Graphs

Journal of Mathematics ◽

10.1155/2020/1023175 ◽

2020 ◽

Vol 2020 ◽

pp. 1-7

Author(s):

Tanveer Iqbal ◽

Muhammad Naeem Azhar ◽

Syed Ahtsham Ul Haq Bokhary

Keyword(s):

Bipartite Graph ◽

Connected Graph ◽

Complete Bipartite Graph ◽

Petersen Graph ◽

Metric Dimension ◽

Resolving Set ◽

Generalized Petersen Graph

In this paper, a new concept k -size edge resolving set for a connected graph G in the context of resolvability of graphs is defined. Some properties and realizable results on k -size edge resolvability of graphs are studied. The existence of this new parameter in different graphs is investigated, and the k -size edge metric dimension of path, cycle, and complete bipartite graph is computed. It is shown that these families have unbounded k -size edge metric dimension. Furthermore, the k-size edge metric dimension of the graphs Pm □ Pn, Pm □ Cn for m, n ≥ 3 and the generalized Petersen graph is determined. It is shown that these families of graphs have constant k -size edge metric dimension.

Download Full-text

Determining the edge metric dimension of the generalized Petersen graph P(n, 3)

Journal of Combinatorial Optimization ◽

10.1007/s10878-021-00780-8 ◽

2021 ◽

Author(s):

David G. L. Wang ◽

Monica M. Y. Wang ◽

Shiqiang Zhang

Keyword(s):

Petersen Graph ◽

Metric Dimension ◽

Generalized Petersen Graph

Download Full-text

On the Local Adjacency Metric Dimension of Generalized Petersen Graphs

CAUCHY ◽

10.18860/ca.v6i1.6487 ◽

2019 ◽

Vol 6 (1) ◽

pp. 10

Author(s):

Marsidi Marsidi ◽

Dafik Dafik ◽

Ika Hesti Agustin ◽

Ridho Alfarisi

Keyword(s):

Petersen Graph ◽

Metric Dimension ◽

Resolving Set ◽

Generalized Petersen Graph ◽

Generalized Petersen Graphs ◽

Neighboring Vertex ◽

Petersen Graphs ◽

Metric Basis ◽

Order Set

<p class="Abstract">The local adjacency metric dimension is one of graph topic. Suppose there are three neighboring vertex , , in path . Path is called local if where each has representation: a is not equals and may equals to . Let’s say, . For an order set of vertices , the adjacency representation of with respect to is the ordered -tuple , where represents the adjacency distance . The distance defined by 0 if , 1 if adjacent with , and 2 if does not adjacent with . The set is a local adjacency resolving set of if for every two distinct vertices , and adjacent with y then . A minimum local adjacency resolving set in is called local adjacency metric basis. The cardinality of vertices in the basis is a local adjacency metric dimension of , denoted by . Next, we investigate the local adjacency metric dimension of generalized petersen graph.</p>

Download Full-text

Mixed metric dimension of graphs with edge disjoint cycles

Discrete Applied Mathematics ◽

10.1016/j.dam.2021.05.004 ◽

2021 ◽

Vol 300 ◽

pp. 1-8

Author(s):

Jelena Sedlar ◽

Riste Škrekovski

Keyword(s):

Metric Dimension ◽

Edge Disjoint ◽

Disjoint Cycles ◽

Mixed Metric

Download Full-text

On cyclic decompositions of the complete graph into the bipartite generalized Petersen graph P(n,3)

Discrete Mathematics ◽

10.1016/j.disc.2021.112339 ◽

2021 ◽

Vol 344 (5) ◽

pp. 112339

Author(s):

Wannasiri Wannasit

Keyword(s):

Complete Graph ◽

Petersen Graph ◽

Generalized Petersen Graph

Download Full-text

The Generalized Connectivity of Generalized Petersen Graph

Journal of Interconnection Networks ◽

10.1142/s0219265921500213 ◽

2021 ◽

Author(s):

Yuan Si ◽

Ping Li ◽

Yuzhi Xiao ◽

Jinxia Liang

Keyword(s):

Steiner Trees ◽

Petersen Graph ◽

Generalized Petersen Graph ◽

Edge Disjoint ◽

Generalized Connectivity ◽

Vertex Set

For a vertex set [Formula: see text] of [Formula: see text], we use [Formula: see text] to denote the maximum number of edge-disjoint Steiner trees of [Formula: see text] such that any two of such trees intersect in [Formula: see text]. The generalized [Formula: see text]-connectivity of [Formula: see text] is defined as [Formula: see text]. We get that for any generalized Petersen graph [Formula: see text] with [Formula: see text], [Formula: see text] when [Formula: see text]. We give the values of [Formula: see text] for Petersen graph [Formula: see text], where [Formula: see text], and the values of [Formula: see text] for generalized Petersen graph [Formula: see text], where [Formula: see text] and [Formula: see text].

Download Full-text