scholarly journals The Locating-Chromatic Number of Origami Graphs

Algorithms ◽  
2021 ◽  
Vol 14 (6) ◽  
pp. 167
Author(s):  
Agus Irawan ◽  
Asmiati Asmiati ◽  
La Zakaria ◽  
Kurnia Muludi
Keyword(s):  
Chromatic Number ◽  
Outer Edge ◽  
Partition Dimension

The locating-chromatic number of a graph combines two graph concepts, namely coloring vertices and partition dimension of a graph. The locating-chromatic number is the smallest k such that G has a locating k-coloring, denoted by χL(G). This article proposes a procedure for obtaining a locating-chromatic number for an origami graph and its subdivision (one vertex on an outer edge) through two theorems with proofs.

scholarly journals On the Locating Chromatic Number of Barbell Shadow Path Graph

2021 ◽  
Vol 5 (2) ◽  
pp. 82
Author(s):  
A. Asmiati ◽  
Maharani Damayanti ◽  
Lyra Yulianti
Keyword(s):  
Chromatic Number ◽  
Path Graph ◽  
Partition Dimension

The locating-chromatic number was introduced by Chartrand in 2002. The locating chromatic number of a graph is a combined concept between the coloring and partition dimension of a graph. The locating chromatic number of a graph is defined as the cardinality of the minimum color classes of the graph. In this paper, we discuss about the locating-chromatic number of shadow path graph and barbell graph containing shadow graph.

scholarly journals The locating-chromatic number and partition dimension of fibonacene graphs

2020 ◽  
Vol 3 (2) ◽  
pp. 116 ◽  
Author(s):  
Ratih Suryaningsih ◽  
Edy Tri Baskoro
Keyword(s):  
Chromatic Number ◽  
Fibonacci Numbers ◽  
Benzenoid Hydrocarbons ◽  
Graph Properties ◽  
Partition Dimension ◽  
Independence Numbers

<p>Fibonacenes are unbranched catacondensed benzenoid hydrocarbons in which all the non-terminal hexagons are angularly annelated. A hexagon is said to be angularly annelated if the hexagon is adjacent to exactly two other hexagons and possesses two adjacent vertices of degree 2. Fibonacenes possess remarkable properties related with Fibonacci numbers. Various graph properties of fibonacenes have been extensively studied, such as their saturation numbers, independence numbers and Wiener indices. In this paper, we show that the locating-chromatic number of any fibonacene graph is 4 and the partition dimension of such a graph is 3.</p>

scholarly journals On the Locating Chromatic Number of Certain Barbell Graphs

2018 ◽  
Vol 2018 ◽  
pp. 1-5
Author(s):  
Asmiati ◽  
I. Ketut Sadha Gunce Yana ◽  
Lyra Yulianti
Keyword(s):  
Chromatic Number ◽  
Graph Partition ◽  
Vertex Set ◽  
Partition Dimension ◽  
Partition Class ◽  
Special Case

The locating chromatic number of a graph G is defined as the cardinality of a minimum resolving partition of the vertex set V(G) such that all vertices have distinct coordinates with respect to this partition and every two adjacent vertices in G are not contained in the same partition class. In this case, the coordinate of a vertex v in G is expressed in terms of the distances of v to all partition classes. This concept is a special case of the graph partition dimension notion. In this paper we investigate the locating chromatic number for two families of barbell graphs.

scholarly journals Locating-chromatic number of the edge-amalgamation of trees

2020 ◽  
Vol 4 (2) ◽  
pp. 126
Author(s):  
Dian Kastika Syofyan ◽  
Edy Tri Baskoro ◽  
Hilda Assiyatun
Keyword(s):  
Chromatic Number ◽  
Upper Bounds ◽  
Title Page ◽  
Metric Dimension ◽  
Chromatic Numbers ◽  
Lower And Upper Bounds ◽  
Vertex Set ◽  
Partition Dimension ◽  
Special Case

<div class="page" title="Page 1"><div class="layoutArea"><div class="column"><p><span>The investigation on the locating-chromatic number of a graph was initiated by Chartrand </span><span>et al. </span><span>(2002). This concept is in fact a special case of the partition dimension of a graph. This topic has received much attention. However, the results are still far from satisfaction. We can define the locating-chromatic number of a graph </span><span>G </span><span>as the smallest integer </span><span>k </span><span>such that there exists a </span><span>k</span><span>-partition of the vertex-set of </span><span>G </span><span>such that all vertices have distinct coordinates with respect to this partition. As we know that the metric dimension of a tree is completely solved. However, the locating-chromatic numbers for most of trees are still open. For </span><span><em>i</em> </span><span>= 1</span><span>, </span><span>2</span><span>, . . . , <em>t</em>, </span><span>let </span><em>T</em><span>i </span><span>be a tree with a fixed edge </span><span>e</span><span>o</span><span>i </span><span>called the terminal edge. The edge-amalgamation of all </span><span>T</span><span>i</span><span>s </span><span>denoted by Edge-Amal</span><span>{</span><span>T</span><span>i</span><span>;</span><span>e</span><span>o</span><span>i</span><span>} </span><span>is a tree formed by taking all the </span><span>T</span><span>i</span><span>s and identifying their terminal edges. In this paper, we study the locating-chromatic number of the edge-amalgamation of arbitrary trees. We give lower and upper bounds for their locating-chromatic numbers and show that the bounds are tight.</span></p></div></div></div>

Quasi-Periodic Oscillations in Dwarf Novae

1979 ◽  
Vol 46 ◽  
pp. 77-88
Author(s):  
Edward L. Robinson
Keyword(s):  
Binary Systems ◽  
Outer Edge ◽  
Light Curves ◽  
Close Binary ◽  
Bright Spot ◽  
Dwarf Novae ◽  
Periodic Oscillations ◽  
High Frequencies ◽  
Short Period ◽  
Typical Time

Three distinct kinds of rapid variations have been detected in the light curves of dwarf novae: rapid flickering, short period coherent oscillations, and quasi-periodic oscillations. The rapid flickering is seen in the light curves of most, if not all, dwarf novae, and is especially apparent during minimum light between eruptions. The flickering has a typical time scale of a few minutes or less and a typical amplitude of about .1 mag. The flickering is completely random and unpredictable; the power spectrum of flickering shows only a slow decrease from low to high frequencies. The observations of U Gem by Warner and Nather (1971) showed conclusively that most of the flickering is produced by variations in the luminosity of the bright spot near the outer edge of the accretion disk around the white dwarf in these close binary systems.

Packing Chromatic Number of Cycle Related Graphs

2014 ◽  
Vol 4 (1) ◽  
pp. 27
Author(s):  
Albert William ◽  
Roy Santiago ◽  
Indra Rajasingh
Keyword(s):  
Chromatic Number ◽  
Packing Chromatic Number

Packing coloring on subdivision-vertex and subdivision-edge join of cycle Cm with path Pn

2020 ◽  
pp. 627-634
Author(s):  
K. Rajalakshmi ◽  
M. Venkatachalam ◽  
M. Barani ◽  
D. Dafik
Keyword(s):  
Chromatic Number ◽  
Path Graph ◽  
Packing Chromatic Number ◽  
Cycle Graph

The packing chromatic number $\chi_\rho$ of a graph $G$ is the smallest integer $k$ for which there exists a mapping $\pi$ from $V(G)$ to $\{1,2,...,k\}$ such that any two vertices of color $i$ are at distance at least $i+1$. In this paper, the authors find the packing chromatic number of subdivision vertex join of cycle graph with path graph and subdivision edge join of cycle graph with path graph.

Bounds on the partition dimension of convex polytopes

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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