scholarly journals b-chromatic number of extended corona of some graphs

2020 ◽  
Vol 7 (2) ◽  
pp. 114-117
Author(s):  
Kiruthika S ◽  
Mohanapriya N
Keyword(s):  
Chromatic Number ◽  
Star Graph

In this paper we find out the b-chromatic number for the extended corona of path with complete on the same order Pn.kn path on order n with star graph on order n+1 say ,Pn.kn+1 cycle with complete on the same order ,Cn.kn cycle on order n with star graph on order n+1 say Cn.kn+1, star graph on order n+1 with complete on order n say kn+1.Kn ,complete on order n with star graph on b-coloring, b-chromatic number, extended corona. order n+1 say kn.Kn+1 respectively.

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 A Research of Achromatic and B-Chromatic Number of Multistar-Related Graphs

2019 ◽  
Vol 8 (6S) ◽  
pp. 141-144
Keyword(s):  
Structural Properties ◽  
Chromatic Number ◽  
Double Star ◽  
Star Graph ◽  
Triple Star

The structural properties, achromatic number and b-chromatic number of central graph of double star graph and triple star graph have been studied in [6]. In this paper, these studies have been carried out, for the central graph of any multi star graph and central graph of shadow graph of star graph and double star graph.

INTERSECTION GRAPH OF SUBMODULES OF A MODULE

2012 ◽  
Vol 11 (01) ◽  
pp. 1250019 ◽  
Author(s):  
S. AKBARI ◽  
H. A. TAVALLAEE ◽  
S. KHALASHI GHEZELAHMAD
Keyword(s):  
Bipartite Graph ◽  
Chromatic Number ◽  
Clique Number ◽  
Simple Graph ◽  
Intersection Graph ◽  
Star Graph ◽  
Graph Theoretic ◽  
Nonzero Intersection ◽  
One To One

Let R be a ring with identity and M be a unitary left R-module. The intersection graph of an R-moduleM, denoted by G(M), is defined to be the undirected simple graph whose vertices are in one to one correspondence with all non-trivial submodules of M and two distinct vertices are adjacent if and only if the corresponding submodules of M have nonzero intersection. We investigate the interplay between the module-theoretic properties of M and the graph-theoretic properties of G(M). We characterize all modules for which the intersection graph of submodules is connected. Also the diameter and the girth of G(M) are determined. We study the clique number and the chromatic number of G(M). Among other results, it is shown that if G(M) is a bipartite graph, then G(M) is a star graph.

scholarly journals ON STAR COLORING OF DEGREE SPLITTING OF COMB PRODUCT GRAPHS

2020 ◽  
pp. 507
Author(s):  
Ulagammal Subramanian ◽  
Vernold Vivin Joseph
Keyword(s):  
Chromatic Number ◽  
Complete Graph ◽  
Vertex Coloring ◽  
Star Graph ◽  
Path Graph ◽  
Product Graphs ◽  
Star Coloring ◽  
Splitting Graph ◽  
Proper Vertex

A star coloring of a graph G is a proper vertex coloring in which every path on four vertices in G is not bicolored. The star chromatic number χs (G) of G is the least number of colors needed to star color G. Let G = (V,E) be a graph with V = S1 [ S2 [ S3 [ . . . [ St [ T where each Si is a set of all vertices of the same degree with at least two elements and T =V (G) − St i=1 Si. The degree splitting graph DS (G) is obtained by adding vertices w1,w2, . . .wt and joining wi to each vertex of Si for 1 i t. The comb product between two graphs G and H, denoted by G ⊲ H, is a graph obtained by taking one copy of G and |V (G)| copies of H and grafting the ith copy of H at the vertex o to the ith vertex of G. In this paper, we give the exact value of star chromatic number of degree splitting of comb product of complete graph with complete graph, complete graph with path, complete graph with cycle, complete graph with star graph, cycle with complete graph, path with complete graph and cycle with path graph.

scholarly journals Power Dominator Chromatic Number for some Special Graphs

2019 ◽  
Vol 8 (12) ◽  
pp. 3957-3960
Keyword(s):  
Chromatic Number ◽  
Star Graph ◽  
Proper Coloring ◽  
Induction Method ◽  
Color Class ◽  
Wheel Graph ◽  
Minimum Number ◽  
Fan Graph ◽  
Multiple Edges ◽  
Dominator Coloring

Let G = (V, E) be a finite, connected, undirected with no loops, multiple edges graph. Then the power dominator coloring of G is a proper coloring of G, such that each vertex of G power dominates every vertex of some color class. The minimum number of color classes in a power dominator coloring of the graph, is the power dominator chromatic number . Here we study the power dominator chromatic number for some special graphs such as Bull Graph, Star Graph, Wheel Graph, Helm graph with the help of induction method and Fan Graph. Suitable examples are provided to exemplify the results.

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 On Dominator Chromatic Number Of Radial Graph Of Some Graphs

2019 ◽  
Vol 6 (2) ◽  
pp. 1-3
Author(s):  
Kalaivani R ◽  
Vijayalakshmi D
Keyword(s):  
Chromatic Number ◽  
Star Graph ◽  
Color Class ◽  
Radial Graph ◽  
Middle Graph ◽  
Dominator Coloring

A dominator coloring is a coloring of the vertices of a graph such that every vertex is either alone in its color class or adjacent to all vertices of at least one other class. In this paper, we obtain the Dominator Chromatic number of the Radial graph for the Central graph of Star graph, Super-radial graph for Middle graph of Cycle and Central graph of Path.

On the r-dynamic coloring of the direct product of a path and a k-subdivision of a star graph

2021 ◽  
pp. 2150121
Author(s):  
Raúl M. Falcón ◽  
M. Venkatachalam ◽  
S. Gowri ◽  
G. Nandini
Keyword(s):  
Chromatic Number ◽  
Direct Product ◽  
Star Graph ◽  
Positive Integers

In this paper, we obtain explicitly the [Formula: see text]-dynamic chromatic number of the direct product of a path [Formula: see text] with a [Formula: see text]-subdivision [Formula: see text] of a star graph, for every positive integers [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text]. Particularly, it is obtained that [Formula: see text].

scholarly journals Maximum Independent Sets Partition of (n,k)-Star Graphs

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-6
Author(s):  
Fu-Tao Hu
Keyword(s):  
Graph Theory ◽  
Chromatic Number ◽  
Computer Modelling ◽  
Independent Sets ◽  
Star Graph ◽  
Star Graphs ◽  
Independent Number ◽  
Two Parameters

The (n,k)-star graph is a very important computer modelling. The independent number and chromatic number of a graph are two important parameters in graph theory. However, we have not known the values of these two parameters of the (n,k)-star graph since it was proposed. In this paper, we show a maximum independent sets partition of (n,k)-star graph. From that, we can immediately deduce the exact value of the independent number and chromatic number of (n,k)-star graph.

scholarly journals PEWARNAAN PADA GRAF BINTANG SIERPINSKI

2017 ◽  
Vol 9 (1) ◽  
pp. 37
Author(s):  
Siti Khabibah
Keyword(s):  
Chromatic Number ◽  
Edge Coloring ◽  
Vertex Coloring ◽  
Star Graph ◽  
Sierpinski Triangle ◽  
Vertex Set

This paper discuss about Sierpinski star graph , which its construction based on the Sierpinski triangle. Vertex set of Sierpinski star graph  is a set of all triangles in Sierpinski triangle; and the edge set of Sierpinski star graph is a set of  all  sides that are joint edges of  two triangles on Sierpinski triangle. From the vertex and edge coloring of Sierpinski star graph, it is found that the chromatic number on vertex coloring of graph  is 1 for n = 1 and 2 for ; while the chromatic number on edge coloring of graf    is 0 for n = 1 and  for

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