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 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 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.

scholarly journals Dimensi Metrik Kuat Lokal Graf Hasil Operasi Kali Kartesian

2020 ◽  
Vol 1 (2) ◽  
pp. 64
Author(s):  
Nurma Ariska Sutardji ◽  
Liliek Susilowati ◽  
Utami Dyah Purwati
Keyword(s):  
Graph Theory ◽  
Cartesian Product ◽  
Metric Dimension ◽  
Star Graph ◽  
Product Graph ◽  
Path Graph ◽  
Strong Metric Dimension ◽  
Metric Dimensions ◽  
Development Result ◽  
Corona Product

The strong local metric dimension is the development result of a strong metric dimension study, one of the study topics in graph theory. Some of graphs that have been discovered about strong local metric dimension are path graph, star graph, complete graph, cycle graphs, and the result corona product graph. In the previous study have been built about strong local metric dimensions of corona product graph. The purpose of this research is to determine the strong local metric dimension of cartesian product graph between any connected graph G and H, denoted by dimsl (G x H). In this research, local metric dimension of G x H is influenced by local strong metric dimension of graph G and local strong metric dimension of graph H. Graph G and graph H has at least two order.

Diagnosability of Bubble-Sort Star Graphs with Missing Edges

2019 ◽  
Vol 19 (02) ◽  
pp. 1950002 ◽  
Author(s):  
SHIYING WANG ◽  
YINGYING WANG
Keyword(s):  
Multiprocessor System ◽  
Star Graph ◽  
Star Graphs ◽  
Comparison Model ◽  
Model Following ◽  
Strong Property

The diagnosability of a multiprocessor system plays an important role. The bubble-sort star graph BSn has many good properties. In this paper, we study the diagnosis on BSn under the comparison model. Following the concept of the local diagnosability, the strong local diagnosability property is discussed. This property describes the equivalence of the local diagnosability of a node and its degree. We prove that BSn (n ≥ 5) has this property, and it keeps this strong property even if there exist (2n − 5) missing edges in it, and the result is optimal with respect to the number of missing edges.

A Note of Independent Number and Domination Number of Qn,k,m-Graph

2019 ◽  
Vol 29 (03) ◽  
pp. 1950011
Author(s):  
Jiafei Liu ◽  
Shuming Zhou ◽  
Zhendong Gu ◽  
Yihong Wang ◽  
Qianru Zhou
Keyword(s):  
Interconnection Networks ◽  
Interconnection Network ◽  
Domination Number ◽  
Multiprocessor System ◽  
Star Graph ◽  
Minimum Cardinality ◽  
Arrangement Graph ◽  
Independent Number ◽  
Potential Applications ◽  
By Products

The independent number and domination number are two essential parameters to assess the resilience of the interconnection network of multiprocessor systems which is usually modeled by a graph. The independent number, denoted by [Formula: see text], of a graph [Formula: see text] is the maximum cardinality of any subset [Formula: see text] such that no two elements in [Formula: see text] are adjacent in [Formula: see text]. The domination number, denoted by [Formula: see text], of a graph [Formula: see text] is the minimum cardinality of any subset [Formula: see text] such that every vertex in [Formula: see text] is either in [Formula: see text] or adjacent to an element of [Formula: see text]. But so far, determining the independent number and domination number of a graph is still an NPC problem. Therefore, it is of utmost importance to determine the number of independent and domination number of some special networks with potential applications in multiprocessor system. In this paper, we firstly resolve the exact values of independent number and upper and lower bound of domination number of the [Formula: see text]-graph, a common generalization of various popular interconnection networks. Besides, as by-products, we derive the independent number and domination number of [Formula: see text]-star graph [Formula: see text], [Formula: see text]-arrangement graph [Formula: see text], as well as three special graphs.

scholarly journals On the Nodal Structure of Nonlinear Stationary Waves on Star Graphs

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 185
Author(s):  
Ram Band ◽  
Sven Gnutzmann ◽  
August Krueger
Keyword(s):  
Existence Of Solutions ◽  
Stationary Waves ◽  
Star Graph ◽  
Oscillation Theorem ◽  
Nodal Domains ◽  
Nodal Structure ◽  
Star Graphs ◽  
Spectral Curves ◽  
Nonlinear Quantum ◽  
Cubic Nonlinear Schrödinger Equation

We consider stationary waves on nonlinear quantum star graphs, i.e., solutions to the stationary (cubic) nonlinear Schrödinger equation on a metric star graph with Kirchhoff matching conditions at the centre. We prove the existence of solutions that vanish at the centre of the star and classify them according to the nodal structure on each edge (i.e., the number of nodal domains or nodal points that the solution has on each edge). We discuss the relevance of these solutions in more applied settings as starting points for numerical calculations of spectral curves and put our results into the wider context of nodal counting, such as the classic Sturm oscillation theorem.

scholarly journals On θ-commutators and the corresponding non-commuting graphs

2017 ◽  
Vol 15 (1) ◽  
pp. 1530-1538
Author(s):  
S. Shalchi ◽  
A. Erfanian ◽  
M. Farrokhi DG
Keyword(s):  
Chromatic Number ◽  
Independent Sets ◽  
Graphs Of Groups

Abstract The θ-commutators of elements of a group with respect to an automorphism are introduced and their properties are investigated. Also, corresponding to θ-commutators, we define the θ-non-commuting graphs of groups and study their correlations with other notions. Furthermore, we study independent sets in θ-non-commuting graphs, which enable us to evaluate the chromatic number of such graphs.

EMBEDDING OF CYCLES AND GRIDS IN STAR GRAPHS

1991 ◽  
Vol 01 (01) ◽  
pp. 43-74 ◽  
Author(s):  
JUNG-SING JWO ◽  
S. LAKSHMIVARAHAN ◽  
S. K. DHALL
Keyword(s):  
Hamiltonian Cycle ◽  
Parallel Computers ◽  
Star Graph ◽  
Attractive Feature ◽  
Star Graphs ◽  
New Class ◽  
Number Of Authors

The use of the star graph as a viable interconnection scheme for parallel computers has been examined by a number of authors in recent times. An attractive feature of this class of graphs is that it has sublogarithmic diameter and has a great deal of symmetry akin to the binary hypercube. In this paper we describe a new class of algorithms for embedding (a) Hamiltonian cycle (b) the set of all even cycles and (c) a variety of two- and multi-dimensional grids in a star graph. In addition, we also derive an algorithm for the ranking and the unranking problem with respect to the Hamiltonian cycle.

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