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

2020 ◽  
Vol 8 ◽  
Author(s):  
Hassan Raza ◽  
Ying Ji
Keyword(s):  
Petersen Graph ◽  
Metric Dimension ◽  
Generalized Petersen Graph ◽  
Mixed Metric

scholarly journals The K -Size Edge Metric Dimension of Graphs

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.

scholarly journals On the Local Adjacency Metric Dimension of Generalized Petersen Graphs

CAUCHY ◽  
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>

scholarly journals Mixed metric dimension of graphs with edge disjoint cycles

2021 ◽  
Vol 300 ◽  
pp. 1-8
Author(s):  
Jelena Sedlar ◽  
Riste Škrekovski
Keyword(s):  
Metric Dimension ◽  
Edge Disjoint ◽  
Disjoint Cycles ◽  
Mixed Metric

The Generalized Connectivity of Generalized Petersen Graph

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].

scholarly journals Mixed metric dimension of graphs

2017 ◽  
Vol 314 ◽  
pp. 429-438 ◽  
Author(s):  
Aleksander Kelenc ◽  
Dorota Kuziak ◽  
Andrej Taranenko ◽  
Ismael G. Yero
Keyword(s):  
Metric Dimension ◽  
Mixed Metric

scholarly journals Multiset and Mixed Metric Dimension for Starphene and Zigzag-Edge Coronoid

2021 ◽  
pp. 1-15
Author(s):  
Jia-Bao Liu ◽  
Sunny Kumar Sharma ◽  
Vijay Kumar Bhat ◽  
Hassan Raza
Keyword(s):  
Metric Dimension ◽  
Zigzag Edge ◽  
Mixed Metric

scholarly journals On Mixed Metric Dimension of Rotationally Symmetric Graphs

IEEE Access ◽  
2020 ◽  
Vol 8 ◽  
pp. 11560-11569 ◽  
Author(s):  
Hassan Raza ◽  
Jia-Bao Liu ◽  
Shaojian Qu
Keyword(s):  
Metric Dimension ◽  
Symmetric Graphs ◽  
Rotationally Symmetric ◽  
Mixed Metric
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