scholarly journals Dominator Coloring on Star and Double Star Graph Families

2012 ◽  
Vol 48 (3) ◽  
pp. 22-25 ◽  
Author(s):  
K. Kavitha ◽  
N.G. David
Keyword(s):  
Double Star ◽  
Star Graph ◽  
Graph Families ◽  
Dominator Coloring

scholarly journals Harmonious coloring on double star graph families

2012 ◽  
Vol 43 (2) ◽  
pp. 153-158 ◽  
Author(s):  
Vernold Vivin.J ◽  
Venkatachalam M. ◽  
Kaliraj K.
Keyword(s):  
Chromatic Number ◽  
Line Graph ◽  
Double Star ◽  
Star Graph ◽  
Graph Families

In this present paper, we have proved for the line graph of double star graph, the harmonious chromatic number and the achromatic number are equal. As a motivation this work can be extended by classifying the different families of graphs for which these two numbers are equal.

scholarly journals Acyclic Coloring on Double Star Graph Families

2012 ◽  
Vol 42 (18) ◽  
pp. 32-35
Author(s):  
R. Arundhadhi ◽  
R. Sattanathan
Keyword(s):  
Double Star ◽  
Star Graph ◽  
Acyclic Coloring ◽  
Graph Families

scholarly journals Harmonious coloring on double star graph families

2012 ◽  
Vol 43 (2) ◽  
Author(s):  
Vernold Vivin.J ◽  
Venkatachalam M. ◽  
Kaliraj K.
Keyword(s):  
Double Star ◽  
Star Graph ◽  
Graph Families

scholarly journals Star Coloring on Double Star Graph Families

2011 ◽  
Vol 5 (1) ◽  
pp. 33-36
Author(s):  
M. Venkatacha ◽  
N. Mohanapriy ◽  
J. Vernold Vivin
Keyword(s):  
Double Star ◽  
Star Graph ◽  
Star Coloring ◽  
Graph Families

scholarly journals Graceful and Magic Labeling in Special Fuzzy Graphs

2019 ◽  
Vol 8 (3) ◽  
pp. 5320-5328
Keyword(s):  
Double Star ◽  
Star Graph ◽  
Fuzzy Graphs

In this paper, we present an algorithm to find fuzzy labeling of a star graph K1,n , bi star graph Bn,n and double star graph K1,n,n . We prove that star graph K1,n at most 89 edges are fuzzy graceful iff it admits fuzzy magic graph. Also we prove that bi star graph Bn,n having at most 59 edges are fuzzy graceful iff it is a fuzzy bi magic graph .We prove that fuzzy labeled double star graph K1,n,n at most 30 edges is fuzzy graceful.

scholarly journals The diachromatic number of double star graph

2021 ◽  
Vol 2106 (1) ◽  
pp. 012024
Author(s):  
Nilamsari Kusumastuti ◽  
Raventino ◽  
Fransiskus Fran
Keyword(s):  
Oriented Graph ◽  
Internal Vertex ◽  
Double Star ◽  
Star Graph

Abstract We are interested in the extension for the concept of complete colouring for oriented graph G → that has been proposed in many different notions by several authors (Edwards, Sopena, and Araujo-Pardo in 2013, 2014, and 2018, respectively). An oriented colouring is complete if for every ordered pair of colours, at least one arc in G → whose endpoints are coloured with these colours. The diachromatic number, dac ( G → ) , is the greatest number of colours in a complete oriented colouring. In this paper, we establish the formula of diachromatic numbers for double star graph, k 1 , n , n → , over all possible orientations on the graph. In particular, if din (u) = 0 (resp. dout(u) = 0)and din (wi ) = 1 (resp. dout (w 1) = 1) for all i, then dac ( k 1 , n , n → ) = ⌊ n ⌋ + 1 , where u is the internal vertex and w i , i ∈ {1,…, n}, is the pendant vertices of the digraph.

THE PERMUTATIONAL GRAPH: A NEW NETWORK TOPOLOGY

1998 ◽  
Vol 09 (01) ◽  
pp. 3-11
Author(s):  
SATOSHI OKAWA
Keyword(s):  
Network Topology ◽  
Equivalence Classes ◽  
Star Graph ◽  
Complete Graphs ◽  
Graph Topology ◽  
Star Graphs ◽  
Network Topologies ◽  
Graph Families ◽  
The Relationship ◽  
Better Than

This paper introduces the penmutational graph, a new network topology, which preserves the same desirable properties as those of a star graph topology. A permutational graph can be decomposed into subgraphs induced by node sets defined by equivalence classes. Using this decomposition, its structual properties as well as the relationship among graph families, permutational graphs, star graphs, and complete graphs are studied. Moreover, the diameters of permutational graphs are investigated and good estimates are obtained which are better than those of some network topologies of similar orders.

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.

scholarly journals Acyclic Colouring of Star Graph Families

2010 ◽  
Vol 7 (2) ◽  
pp. 31-33
Author(s):  
K. Thilagavathi ◽  
P. Shanas Babu
Keyword(s):  
Star Graph ◽  
Graph Families
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