scholarly journals Different Types of Neutrosophic Chromatic Number

2021 ◽  
Author(s):  
Henry Garrett
Keyword(s):  
Graph Theory ◽  
Chromatic Number ◽  
Chromatic Numbers ◽  
Common Edge ◽  
Specific Relation ◽  
Different Types ◽  
Neutrosophic Graph

New setting is introduced to study chromatic number. Different types of chromatic numbers and neutrosophic chromatic number are proposed in this way, some results are obtained. Classes of neutrosophic graphs are used to obtains these numbers and the representatives of the colors. Using colors to assign to the vertices of neutrosophic graphs is applied. Some questions and problems are posed concerning ways to do further studies on this topic. Using different types of edges from connectedness in same neutrosophic graphs and in modified neutrosophic graphs to define the relation amid vertices which implies having different colors amid them and as consequences, choosing one vertex as a representative of each color to use them in a set of representatives and finally, using neutrosophic cardinality of this set to compute types of chromatic numbers. This specific relation amid edges is necessary to compute both types of chromatic number concerning the number of representative in the set of representatives and types of neutrosophic chromatic number concerning neutrosophic cardinality of set of representatives. If two vertices have no intended edge, then they can be assigned to same color even they’ve common edge. Basic familiarities with neutrosophic graph theory and graph theory are proposed for this article.

scholarly journals Neutrosophic Chromatic Number Based on Connectedness

2021 ◽  
Author(s):  
Henry Garrett
Keyword(s):  
Graph Theory ◽  
Chromatic Number ◽  
Common Edge ◽  
Specific Relation ◽  
Neutrosophic Graph

New setting is introduced to study chromatic number. vital chromatic number and n-vital chromatic number are proposed in this way, some results are obtained. Classes of neutrosophic graphs are used to obtains these numbers and the representatives of the colors. Using colors to assign to the vertices of neutrosophic graphs is applied. Some questions and problems are posed concerning ways to do further studies on this topic. Using vital edge from connectedness to define the relation amid vertices which implies having different colors amid them and as consequences, choosing one vertex as a representative of each color to use them in a set of representatives and finally, using neutrosophic cardinality of this set to compute vital chromatic number. This specific relation amid edges is necessary to compute both vital chromatic number concerning the number of representative in the set of representatives and n-vital chromatic number concerning neutrosophic cardinality of set of representatives. If two vertices have no vital edge, then they can be assigned to same color even they’ve common edge. Basic familiarities with neutrosophic graph theory and graph theory are proposed for this article.

scholarly journals Chromatic Number and Neutrosophic Chromatic Number

2021 ◽  
Author(s):  
Henry Garrett
Keyword(s):  
Graph Theory ◽  
Chromatic Number ◽  
Common Edge ◽  
Specific Relation ◽  
Neutrosophic Graph

New setting is introduced to study chromatic number. Neutrosophic chromatic number and chromatic number are proposed in this way, some results are obtained. Classes of neutrosophic graphs are used to obtains these numbers and the representatives of the colors. Using colors to assigns to the vertices of neutrosophic graphs is applied. Some questions and problems are posed concerning ways to do further studies on this topic. Using strong edge to define the relation amid vertices which implies having different colors amid them and as consequences, choosing one vertex as a representative of each color to use them in a set of representatives and finally, using neutrosophic cardinality of this set to compute neutrosophic chromatic number. This specific relation amid edges is necessary to compute both chromatic number concerning the number of representative in the set of representatives and neutrosophic chromatic number concerning neutrosophic cardinality of set of representatives. If two vertices have no strong edge, then they can be assigned to same color even they’ve common edge. Basic familiarities with neutrosophic graph theory and graph theory are proposed for this article.

scholarly journals Determination of Fractional Chromatic Numbers in the Operation of Adding Two Different Graphs

2022 ◽  
Vol 18 (2) ◽  
pp. 161-168
Author(s):  
Junianto Sesa ◽  
Siswanto Siswanto
Keyword(s):  
Graph Theory ◽  
Chromatic Number ◽  
Index Theory ◽  
Chromatic Numbers ◽  
Fractional Chromatic Number ◽  
Path Graph ◽  
Fractional Coloring ◽  
Different Color ◽  
Cycle Graph

The development of graph theory has provided many new pieces of knowledge, one of them is graph color. Where the application is spread in various fields such as the coding index theory. Fractional coloring is multiple coloring at points with different colors where the adjoining point has a different color. The operation in the graph is known as the sum operation. Point coloring can be applied to graphs where the result of operations is from several special graphs.  In this case, the graph summation results of the path graph and the cycle graph will produce the same fractional chromatic number as the sum of the fractional chromatic numbers of each graph before it is operated.

scholarly journals Metric Dimension in fuzzy(neutrosophic) Graphs-VII

2021 ◽  
Author(s):  
Henry Garrett
Keyword(s):  
Graph Theory ◽  
Individual Case ◽  
Metric Dimension ◽  
Neutrosophic Graph ◽  
Distinct Distance ◽  
Optimal Set ◽  
Dimension Number

New notion of dimension as set, as two optimal numbers including metric number, dimension number and as optimal set are introduced in individual framework and in formation of family. Behaviors of twin and antipodal are explored in fuzzy(neutrosophic) graphs. Fuzzy(neutrosophic) graphs, under conditions, fixed-edges, fixed-vertex and strong fixed-vertex are studied. Some classes as path, cycle, complete, strong, t-partite, bipartite, star and wheel in the formation of individual case and in the case, they form a family are studied in the term of dimension. Fuzzification(neutrosofication) of twin vertices but using crisp concept of antipodal vertices are another approaches of this study. Thus defining two notions concerning vertices which one of them is fuzzy(neutrosophic) titled twin and another is crisp titled antipodal to study the behaviors of cycles which are partitioned into even and odd, are concluded. Classes of cycles according to antipodal vertices are divided into two classes as even and odd. Parity of the number of edges in cycle causes to have two subsections under the section is entitled to antipodal vertices. In this study, the term dimension is introduced on fuzzy(neutrosophic) graphs. The locations of objects by a set of some junctions which have distinct distance from any couple of objects out of the set, are determined. Thus it’s possible to have the locations of objects outside of this set by assigning partial number to any objects. The classes of these specific graphs are chosen to obtain some results based on dimension. The types of crisp notions and fuzzy(neutrosophic) notions are used to make sense about the material of this study and the outline of this study uses some new notions which are crisp and fuzzy(neutrosophic). Some questions and problems are posed concerning ways to do further studies on this topic. Basic familiarities with fuzzy(neutrosophic) graph theory and graph theory are proposed for this article.

scholarly journals Body Mass Index in Human Walking on Different Types of Soil Using Graph Theory

IEEE Access ◽  
2018 ◽  
Vol 6 ◽  
pp. 47935-47942
Author(s):  
Washington Velasquez ◽  
Manuel S. Alvarez-Alvarado ◽  
Joaquin Salvachua
Keyword(s):  
Body Mass Index ◽  
Graph Theory ◽  
Body Mass ◽  
Human Walking ◽  
Different Types

On the Babai and Upper Chromatic Numbers of Graphs of Diameter 2

2021 ◽  
Vol 52 (1) ◽  
pp. 113-123
Author(s):  
Peter Johnson ◽  
Alexis Krumpelman
Keyword(s):  
Chromatic Number ◽  
Metric Space ◽  
Simple Graph ◽  
Chromatic Numbers

The Babai numbers and the upper chromatic number are parameters that can be assigned to any metric space. They can, therefore, be assigned to any connected simple graph. In this paper we make progress in the theory of the first Babai number and the upper chromatic number in the simple graph setting, with emphasis on graphs of diameter 2.

scholarly journals Interval-Valued Fuzzy Soft Graphs

2017 ◽  
Vol 5 (1) ◽  
pp. 19-27 ◽  
Author(s):  
Onur Zihni ◽  
Yıldıray Çelik ◽  
Güven Kara
Keyword(s):  
Graph Theory ◽  
Cartesian Product ◽  
Soft Sets ◽  
Strong Product ◽  
Different Types ◽  
Fuzzy Soft Sets ◽  
Interval Valued

Abstract In this paper, we combine concepts of interval-valued fuzzy soft sets and graph theory. Then we introduce notations of interval-valued fuzzy soft graphs and complete interval-valued fuzzy soft graphs. We also present several different types operations including cartesian product, strong product and composition on interval-valued fuzzy soft graphs and investigate some properties of them.

On the Adjacent Vertex Distinguishing Proper Edge Colorings of Several Classes of Complete 5-Partite Graphs

2013 ◽  
Vol 333-335 ◽  
pp. 1452-1455
Author(s):  
Chun Yan Ma ◽  
Xiang En Chen ◽  
Fang Yang ◽  
Bing Yao
Keyword(s):  
Chromatic Number ◽  
Edge Coloring ◽  
Adjacent Vertex ◽  
Chromatic Numbers ◽  
Edge Colorings ◽  
Proper Edge Coloring ◽  
Minimum Number

A proper $k$-edge coloring of a graph $G$ is an assignment of $k$ colors, $1,2,\cdots,k$, to edges of $G$. For a proper edge coloring $f$ of $G$ and any vertex $x$ of $G$, we use $S(x)$ denote the set of thecolors assigned to the edges incident to $x$. If for any two adjacent vertices $u$ and $v$ of $G$, we have $S(u)\neq S(v)$,then $f$ is called the adjacent vertex distinguishing proper edge coloring of $G$ (or AVDPEC of $G$ in brief). The minimum number of colors required in an AVDPEC of $G$ is called the adjacent vertex distinguishing proper edge chromatic number of $G$, denoted by $\chi^{'}_{\mathrm{a}}(G)$. In this paper, adjacent vertex distinguishing proper edge chromatic numbers of several classes of complete 5-partite graphs are obtained.

PARALLEL VERTEX COLOURING OF INTERVAL GRAPHS

1999 ◽  
Vol 10 (01) ◽  
pp. 19-31 ◽  
Author(s):  
G. SAJITH ◽  
SANJEEV SAXENA
Keyword(s):  
Chromatic Number ◽  
Interval Graph ◽  
Interval Graphs ◽  
Chromatic Numbers ◽  
Erew Pram ◽  
Pram Model ◽  
Interval Representation ◽  
Left And Right ◽  
Crcw Pram ◽  
Vertex Colouring

Evidence is given to suggest that minimally vertex colouring an interval graph may not be in NC 1. This is done by showing that 3-colouring a linked list is NC 1-reducible to minimally colouring an interval graph. However, it is shown that an interval graph with a known interval representation and an O(1) chromatic number can be minimally coloured in NC 1. For the CRCW PRAM model, an o( log n) time, polynomial processors algorithm is obtained for minimally colouring an interval graph with o( log n) chromatic number and a known interval representation. In particular, when the chromatic number is O(( log n)1-ε), 0<ε<1, the algorithm runs in O( log n/ log log n) time. Also, an O( log n) time, O(n) cost, EREW PRAM algorithm is found for interval graphs of arbitrary chromatic numbers. The following lower bound result is also obtained: even when the left and right endpoints of the interval are separately sorted, minimally colouring an interval graph needs Ω( log n/ log log n) time, on a CRCW PRAM, with a polynomial number of processors.

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