scholarly journals All unicyclic graphs of order n with locating-chromatic number n-3

2021 ◽  
Vol 5 (2) ◽  
pp. 73
Author(s):  
Edy Tri Baskoro ◽  
Arfin Arfin

<p class="p1">Characterizing all graphs having a certain locating-chromatic number is not an easy task. In this paper, we are going to pay attention on finding all unicyclic graphs of order <em>n</em> (⩾ 6) and having locating-chromatic number <em>n</em>-3.</p>

2018 ◽  
Vol 2 (1) ◽  
pp. 30 ◽  
Author(s):  
Nuris Hisan Nazula ◽  
S Slamin ◽  
D Dafik

The local antimagic labeling on a graph G with |V| vertices and |E| edges is defined to be an assignment f : E --&gt; {1, 2,..., |E|} so that the weights of any two adjacent vertices u and v are distinct, that is, w(u)̸  ̸= w(v) where w(u) = Σe∈<sub>E(u)</sub> f(e) and E(u) is the set of edges incident to u. Therefore, any local antimagic labeling induces a proper vertex coloring of G where the vertex u is assigned the color w(u). The local antimagic chromatic number, denoted by χla(G), is the minimum number of colors taken over all colorings induced by local antimagic labelings of G. In this paper, we present the local antimagic chromatic number of unicyclic graphs that is the graphs containing exactly one cycle such as kite and cycle with two neighbour pendants.


2019 ◽  
Vol 1306 ◽  
pp. 012039
Author(s):  
R. Alfarisi ◽  
Dafik ◽  
R.M. Prihandini ◽  
R. Adawiyah ◽  
E. R. Albirri ◽  
...  

Author(s):  
Liliana Alcón ◽  
Marisa Gutierrez ◽  
Carmen Hernando ◽  
Mercé Mora ◽  
I. M. Pelayo

Author(s):  
Edgars Rencis ◽  
Janis Barzdins ◽  
Sergejs Kozlovics

Towards Open Graphical Tool-Building Framework Nowadays, there are many frameworks for developing domain-specific tools. However, if we want to create a really sophisticated tool with specific functionality requirements, it is not always an easy task to do. Although tool-building platforms offer some means for extending the tool functionality and accessing it from external applications, it usually requires a deep understanding of various technical implementation details. In this paper we try to go one step closer to a really open graphical tool-building framework that would allow both to change the behavior of the tool and to access the tool from the outside easily. We start by defining a specialization of metamodels which is a great and powerful facility itself. Then we go on and show how this can be applied in the field of graphical domain-specific tool building. The approach is demonstrated on an example of a subset of UML activity diagrams. The benefits of the approach are also clearly indicated. These include a natural and intuitive definition of tools, a strict logic/presentation separation and the openness for extensions as well as for external applications.


Author(s):  
Albert William ◽  
Roy Santiago ◽  
Indra Rajasingh

Author(s):  
K. Rajalakshmi ◽  
M. Venkatachalam ◽  
M. Barani ◽  
D. Dafik

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.


Author(s):  
Kristi A. Olson

What is a fair income distribution? The empirical literature seems to assume that equal income would be fair, but the equal income answer faces two objections. First, equal income is likely to be inefficient. This book sets aside efficiency concerns as a downstream consideration; it seeks to identify a fair distribution. The second objection—pointed out by both leftist political philosopher G. A. Cohen and conservative economist Milton Friedman—is that equal income is unfair to the hardworking. Measuring labor burdens in order to adjust income shares, however, is no easy task. Some philosophers and economists attempt to sidestep the measurement problem by invoking the envy test. Yet a distribution in which no one prefers someone else’s circumstances to her own, as the envy test requires, is unlikely to exist—and, even if it does exist, the normative connection between the envy test and fairness has not been established. The Solidarity Solution provides a novel answer: when someone claims that her situation should be improved at someone else’s expense, she must be able to give a reason that cannot be rejected by a free and equal individual who regards everyone else as the same. Part I develops the solidarity solution and shows that rigorous distributive implications can be derived from a relational ideal. Part II uses the solidarity solution to critique the competing theories of Ronald Dworkin, Philippe Van Parijs, and Marc Fleurbaey. Finally, part III identifies insights for the gender wage gap and taxation.


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