scholarly journals On the r-dynamic coloring of the direct product of a path with either a complete graph or a wheel graph

2021 ◽  
Vol 6 (2) ◽  
pp. 1470-1496
Author(s):  
T. Deepa ◽  
◽  
Raúl M. Falcón ◽  
M. Venkatachalam ◽  
Keyword(s):  
Direct Product ◽  
Complete Graph ◽  
Wheel Graph

b-Chromatic sum of a graph

2015 ◽  
Vol 07 (04) ◽  
pp. 1550040 ◽  
Author(s):  
P. C. Lisna ◽  
M. S. Sunitha
Keyword(s):  
Bipartite Graph ◽  
Chromatic Number ◽  
Complete Graph ◽  
Complete Bipartite Graph ◽  
Double Star ◽  
Star Graph ◽  
Proper Coloring ◽  
Color Class ◽  
Wheel Graph ◽  
Chromatic Sum

A b-coloring of a graph G is a proper coloring of the vertices of G such that there exists a vertex in each color class joined to at least one vertex in each other color classes. The b-chromatic number of a graph G, denoted by [Formula: see text], is the maximum integer [Formula: see text] such that G admits a b-coloring with [Formula: see text] colors. In this paper we introduce a new concept, the b-chromatic sum of a graph [Formula: see text], denoted by [Formula: see text] and is defined as the minimum of sum of colors [Formula: see text] of [Formula: see text] for all [Formula: see text] in a b-coloring of [Formula: see text] using [Formula: see text] colors. Also obtained the b-chromatic sum of paths, cycles, wheel graph, complete graph, star graph, double star graph, complete bipartite graph, corona of paths and corona of cycles.

$$L(1,1)$$ L ( 1 , 1 ) -labelling of the direct product of a complete graph and a cycle

2013 ◽  
Vol 30 (3) ◽  
pp. 803-811 ◽  
Author(s):  
Byeong Moon Kim ◽  
Yoomi Rho ◽  
Byung Chul Song
Keyword(s):  
Direct Product ◽  
Complete Graph

scholarly journals On Divisor 3-Equitable Labeling of Wheel Graphs

2020 ◽  
Vol 8 (5) ◽  
pp. 5480-5483
Keyword(s):  
Complete Graph ◽  
Single Vertex ◽  
Wheel Graph ◽  
Wheel Graphs

A graph 𝑮 on 𝒏 vertices is said to admit a divisor 3- equitable labeling if there exists a bijection 𝒅 ∶ 𝑽(𝑮) → {𝟏, 𝟐, . . . , 𝒏} defined by 𝒅 𝒆 = 𝒙𝒚 = 𝟏,𝒊𝒇𝒅(𝒙)|𝒅 𝒚 or 𝒅 𝒚 |𝒅(𝒙) 𝟐, 𝒊𝒇 𝒅 𝒙 𝒅 𝒚 = 𝟐 𝒐𝒓 𝒅 𝒚 𝒅 𝒙 = 𝟐 𝟎, 𝒐𝒕𝒉𝒆𝒓𝒘𝒊𝒔𝒆 and |𝒆𝒅 𝒊 − 𝒆𝒅 𝒋 | ≤ 𝟏 for all 𝟎 ≤ 𝒊,𝒋 ≤ 𝟐, where 𝒆𝒅 𝒊 denotes the number of edges labelled with “𝒊”. A graph which permits a divisor 3-equitable labeling is called a divisor 3-equitable graph. A wheel graph 𝑾𝒏 is defined as 𝑾𝒏 = 𝑪𝒏−𝟏⋀ 𝑲𝟏, where 𝑪𝒏−𝟏 is a cycle on 𝒏 − 𝟏 vertices and 𝑲𝟏 is a complete graph on a single vertex. In this paper, we prove the non-existence of a divisor 3- equitable labeling of the wheel graph 𝑾𝒏 for 𝒏 ≥ 𝟕.

scholarly journals Vertex Polynomial of Middle, Line and Total Graphs of some standard Graphs

2020 ◽  
Vol 4 (8) ◽  
pp. 86-89
Keyword(s):  
Complete Graph ◽  
Middle Line ◽  
Wheel Graph

In this article, we have obtained vertex polynomial of Middle, Line and Total graphs of some standard graphs namely complete graph, star, path, cycle and wheel graph.

scholarly journals Strong Split Litact Domination in Graphs

2019 ◽  
Vol 8 (3) ◽  
pp. 7296-7300
Keyword(s):  
Complete Graph ◽  
Domination Number ◽  
Limiting Factors ◽  
Wheel Graph ◽  
Domination In Graphs ◽  
The Relationship ◽  
Cycle Graph

In this paper the strong split litact domination number of some standard graphs like Cycle graph , wheel graph , Complete graph , Bi-partite graph etc., are calculated and tried to bring up the relationship between the with different limiting factors of and also with other domination limiting factors of .

Equitable Total Coloring of Direct Product of Path and Cycle

2019 ◽  
Vol 10 (7) ◽  
pp. 1476-1481
Author(s):  
S. Moidheen Aliyar ◽  
S. Manimaran ◽  
K. Manikandan
Keyword(s):  
Direct Product ◽  
Total Coloring

Sport and nationalism in the Republic of North Macedonia

Focaal ◽  
2019 ◽  
pp. 1-13
Author(s):  
Vasiliki P. Neofotistos
Keyword(s):  
Direct Product ◽  
Nation Building ◽  
National History ◽  
Sports Teams ◽  
The Balkans ◽  
The North ◽  
Political Forces ◽  
The Republic

Using the Republic of North Macedonia as a case study, this article analyzes the processes through which national sports teams’ losing performance acquires a broad social and political significance. I explore claims to sporting victory as a direct product of political forces in countries located at the bottom of the global hierarchy that participate in a wider system of coercive rule, frequently referred to as empire. I also analyze how public celebrations of claimed sporting victories are intertwined with nation-building efforts, especially toward the global legitimization of a particular version of national history and heritage. The North Macedonia case provides a fruitful lens through which we can better understand unfolding sociopolitical developments, whereby imaginings of the global interlock with local interests and needs, in the Balkans and beyond.

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