scholarly journals General position problem of hyper tree and shuffle hyper tree networks

2020 ◽  
Author(s):  
R. Prabha ◽  
S. Renukaa Devi
Keyword(s):  
General Position ◽  
Tree Networks ◽  
Position Problem

scholarly journals The general position problem on Kneser graphs and on some graph operations

2019 ◽  
Author(s):  
Modjtaba Ghorbani ◽  
Sandi Klavžar ◽  
Hamid Reza Maimani ◽  
Mostafa Momeni ◽  
Farhad Rahimi Mahid ◽  
...  
Keyword(s):  
General Position ◽  
Graph Operations ◽  
Kneser Graphs ◽  
Position Problem

A GENERAL POSITION PROBLEM IN GRAPH THEORY

2018 ◽  
Vol 98 (2) ◽  
pp. 177-187 ◽  
Author(s):  
PAUL MANUEL ◽  
SANDI KLAVŽAR
Keyword(s):  
Graph Theory ◽  
Lower Bounds ◽  
General Position ◽  
Upper Bounds ◽  
Np Complete ◽  
Position Problem

The paper introduces a graph theory variation of the general position problem: given a graph $G$, determine a largest set $S$ of vertices of $G$ such that no three vertices of $S$ lie on a common geodesic. Such a set is a max-gp-set of $G$ and its size is the gp-number $\text{gp}(G)$ of $G$. Upper bounds on $\text{gp}(G)$ in terms of different isometric covers are given and used to determine the gp-number of several classes of graphs. Connections between general position sets and packings are investigated and used to give lower bounds on the gp-number. It is also proved that the general position problem is NP-complete.

The general position problem and strong resolving graphs

2019 ◽  
Vol 17 (1) ◽  
pp. 1126-1135 ◽  
Author(s):  
Sandi Klavžar ◽  
Ismael G. Yero
Keyword(s):  
Connected Graph ◽  
General Position ◽  
Clique Number ◽  
Bipartite Graphs ◽  
Complete Graphs ◽  
Direct Products ◽  
Strong Product ◽  
Product Graphs ◽  
Complete Bipartite Graphs ◽  
Position Problem

Abstract The general position number gp(G) of a connected graph G is the cardinality of a largest set S of vertices such that no three pairwise distinct vertices from S lie on a common geodesic. It is proved that gp(G) ≥ ω(GSR), where GSR is the strong resolving graph of G, and ω(GSR) is its clique number. That the bound is sharp is demonstrated with numerous constructions including for instance direct products of complete graphs and different families of strong products, of generalized lexicographic products, and of rooted product graphs. For the strong product it is proved that gp(G ⊠ H) ≥ gp(G)gp(H), and asked whether the equality holds for arbitrary connected graphs G and H. It is proved that the answer is in particular positive for strong products with a complete factor, for strong products of complete bipartite graphs, and for certain strong cylinders.

scholarly journals A Steiner general position problem in graph theory

2021 ◽  
Vol 40 (6) ◽  
Author(s):  
Sandi Klavžar ◽  
Dorota Kuziak ◽  
Iztok Peterin ◽  
Ismael G. Yero
Keyword(s):  
Graph Theory ◽  
General Position ◽  
Position Problem

Rationality revisited: Politicisation through planning rationality against the rationality of power

2021 ◽  
pp. 147309522110011
Author(s):  
Esin Özdemir
Keyword(s):  
Public Interest ◽  
General Position ◽  
Strong Relationship ◽  
Planning Theory ◽  
The Political ◽  
Rational Thinking ◽  
Liberal Democracies ◽  
Substantive Issue ◽  
Rational Consensus ◽  
Definition Of

In this article, I readdress the issue of rationality, which has been so far considered in western liberal democracies and in planning theory as procedural, and more recently as post-political in the post-foundational approach, aiming to show how it can gain a substantive and politicising character. I first discuss the problems and limits of the treatment of rational thinking as well as rational consensus-seeking as merely procedural and post-political. Secondly, utilising the notion of Realrationalität of Flyvbjerg, I discuss how rationality attains a politicising role due to its strong relationship with power. Using the concept of planning rationality aiming at public interest, I present the general position and actions of professional organisations in Turkey, focusing on the Chamber of City Planners, as an example illustrative of my argument. I finally argue that rationality becomes a substantive issue that politicizes planning, when it is put forward as an alternative to authoritarian market logic. In doing so, I adopt the Rancièrian definition of the political, defined as disclosure of a wrong and staging of equality. In conclusion, I first emphasize the importance of avoiding quick rejections of the concepts of rationality and consensus in the framework of planning activity and planning theory and secondly, call for a broader definition of the political; the political that is not confined to conflict but is open to rational thinking and rational consensus.

scholarly journals THE GENERAL POSITION NUMBER OF THE CARTESIAN PRODUCT OF TWO TREES

2020 ◽  
pp. 1-10
Author(s):  
JING TIAN ◽  
KEXIANG XU ◽  
SANDI KLAVŽAR
Keyword(s):  
Shortest Path ◽  
Connected Graph ◽  
General Position ◽  
Cartesian Product

Abstract The general position number of a connected graph is the cardinality of a largest set of vertices such that no three pairwise-distinct vertices from the set lie on a common shortest path. In this paper it is proved that the general position number is additive on the Cartesian product of two trees.

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