Total Chromatic Sum for Trees

2020 ◽  
pp. 27-37
Author(s):  
Ewa Kubicka ◽  
Grzegorz Kubicki ◽  
Michał Małafiejski ◽  
Krzysztof M. Ocetkiewicz
Keyword(s):  
Chromatic Sum

scholarly journals Task Scheduling Problem Using Fuzzy Graph

2016 ◽  
Vol 1 (1-2) ◽  
pp. 16-20
Author(s):  
Vivek Raich ◽  
Shweta Rai
Keyword(s):  
Task Scheduling ◽  
Single Machine ◽  
Scheduling Problem ◽  
Scheduling Theory ◽  
Scheduling Problems ◽  
Fuzzy Graph ◽  
Minimum Value ◽  
Chromatic Sum ◽  
Completion Times

The concept of obtaining fuzzy sum of fuzzy colorings problem has a natural application in scheduling theory. The problem of scheduling N jobs on a single machine and obtain the minimum value of the job completion times is equivalent to finding the fuzzy chromatic sum of the fuzzy graph modeled for this problem. The aim of this paper is to solve task scheduling problems using fuzzy graph.

scholarly journals Results on chromatic sum of graphs

2003 ◽  
Author(s):  
Sundararajan Arabhi
Keyword(s):  
Chromatic Sum

On the b-Chromatic Sum of Mycielskian of Km, n, Kn and Cn

2020 ◽  
Vol 20 (02) ◽  
pp. 2050007
Author(s):  
P. C. LISNA ◽  
M. S. SUNITHA
Keyword(s):  
Image Processing ◽  
Chromatic Number ◽  
Bipartite Graphs ◽  
Complete Graphs ◽  
Proper Coloring ◽  
Color Class ◽  
Vertex Set ◽  
Chromatic Sum ◽  
Complete Bipartite Graphs

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 φ(G), is the largest integer k such that G has a b-coloring with k colors. The b-chromatic sum of a graph G(V, E), denoted by φ′(G) is defined as the minimum of sum of colors c(v) of v for all v ∈ V in a b-coloring of G using φ(G) colors. The Mycielskian or Mycielski, μ(H) of a graph H with vertex set {v1, v2,…, vn} is a graph G obtained from H by adding a set of n + 1 new vertices {u, u1, u2, …, un} joining u to each vertex ui(1 ≤ i ≤ n) and joining ui to each neighbour of vi in H. In this paper, the b-chromatic sum of Mycielskian of cycles, complete graphs and complete bipartite graphs are discussed. Also, an application of b-coloring in image processing is discussed here.

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.

New parameters involving chromatic sum in a graph

2009 ◽  
Vol 33 ◽  
pp. 81-86
Author(s):  
Emmanuel Jebarajan ◽  
R. Sundareswaran ◽  
V. Swaminathan
Keyword(s):  
Chromatic Sum

scholarly journals Certain chromatic sums of some cycle-related graph classes

2016 ◽  
Vol 08 (03) ◽  
pp. 1650050 ◽  
Author(s):  
N. K. Sudev ◽  
K. P. Chithra ◽  
Johan Kok
Keyword(s):  
Graph Classes ◽  
Related Graph ◽  
Sum Formula ◽  
Chromatic Sum

Let [Formula: see text] be a certain type of proper [Formula: see text]-coloring of a given graph [Formula: see text] and [Formula: see text] denote the number of times a particular color [Formula: see text] is assigned to the vertices of [Formula: see text]. Then, the coloring sum of a given graph [Formula: see text] with respect to the coloring [Formula: see text], denoted by [Formula: see text] is defined to be [Formula: see text]. The coloring sums such as [Formula: see text]-chromatic sum, [Formula: see text]-chromatic sum, [Formula: see text]-chromatic sum, [Formula: see text]-chromatic sum, etc. are some of these types of coloring sums that have been studied recently. Motivated by these studies on certain chromatic sums of graphs, in this paper, we study certain chromatic sums for some standard cycle-related graphs.

Edge-chromatic sum of trees and bounded cyclicity graphs

2000 ◽  
Vol 75 (1-2) ◽  
pp. 65-69 ◽  
Author(s):  
Krzysztof Giaro ◽  
Marek Kubale
Keyword(s):  
Chromatic Sum
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