The dominating number of a random cubic graph

1995 ◽  
Vol 7 (3) ◽  
pp. 209-221 ◽  
Author(s):  
Michael Molloy ◽  
Bruce Reed
Keyword(s):  
Cubic Graph ◽  
Dominating Number

Perfect Matching Index versus Circular Flow Number of a Cubic Graph

2021 ◽  
Vol 35 (2) ◽  
pp. 1287-1297
Author(s):  
Edita Máčajová ◽  
Martin Škoviera
Keyword(s):  
Perfect Matching ◽  
Cubic Graph ◽  
Flow Number ◽  
Circular Flow ◽  
Matching Index

PEMILIHAN KARIR PADA PEGAWAI GENERASI MILLENIAL (STUDI KASUS : PEGAWAI PT XYZ)

2021 ◽  
Vol 8 (2) ◽  
Author(s):  
FEBRU RADHIANJAYA
Keyword(s):  
Qualitative Research ◽  
Human Resources ◽  
Career Choice ◽  
Millennial Generation ◽  
Career Selection ◽  
Interview Method ◽  
Dominating Number ◽  
Two Factors ◽  
A Company

PT XYZ is a company engaged in the field of production and services that has Human Resources spread throughout Indonesia. In this study, the object of observation is the employee in the East Java Unit which has a total of 2,300 personnel with the composition of the Millennial Generation (born 1981-1994) of 51% as the dominating number of employees in PT XYZ. The results of an interest survey conducted on 698 structural employees at the Basic Supervisor level (managerial type career) at PT XYZ East Java Unit, showed that 25% or 171 employees of the millennial generation chose functional careers (type of expertise). This phenomenon is then explored further in the research objectives, namely what factors influence career selection in millennial generation employees. This research is a qualitative research that uses the interview method. The result is that there are two factors that influence career choice, namely responsibility and type of work.   Keywords : Millenials, Careers, Qualitative

THE CONJUGACY CLASSES OF SOME FINITE METABELIAN GROUPS AND THEIR RELATED GRAPHS

2016 ◽  
Vol 79 (1) ◽  
Author(s):  
Nor Haniza Sarmin ◽  
Ain Asyikin Ibrahim ◽  
Alia Husna Mohd Noor ◽  
Sanaa Mohamed Saleh Omer
Keyword(s):  
Graph Theory ◽  
Conjugacy Class ◽  
Dihedral Group ◽  
Clique Number ◽  
Conjugacy Classes ◽  
Quaternion Group ◽  
Metabelian Groups ◽  
Dominating Number ◽  
Graph Properties ◽  
Class Graph

In this paper, the conjugacy classes of three metabelian groups, namely the Quasi-dihedral group, Dihedral group and Quaternion group of order 16 are computed. The obtained results are then applied to graph theory, more precisely to conjugate graph and conjugacy class graph. Some graph properties such as chromatic number, clique number, dominating number and independent number are found.   

Lower Bounds For Induced Forests in Cubic Graphs

1987 ◽  
Vol 30 (2) ◽  
pp. 193-199 ◽  
Author(s):  
J. A. Bondy ◽  
Glenn Hopkins ◽  
William Staton
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Cubic Graphs ◽  
Cubic Graph

AbstractIf G is a connected cubic graph with ρ vertices, ρ > 4, then G has a vertex-induced forest containing at least (5ρ - 2)/8 vertices. In case G is triangle-free, the lower bound is improved to (2ρ — l)/3. Examples are given to show that no such lower bound is possible for vertex-induced trees.

Tighter Bounds on the Size of a Maximum P 3-Matching in a Cubic Graph

2008 ◽  
Vol 24 (5) ◽  
pp. 461-468 ◽  
Author(s):  
Adrian Kosowski ◽  
Michał Małafiejski ◽  
Paweł Żyliński
Keyword(s):  
Cubic Graph

THE JACOBSON GRAPH OF COMMUTATIVE RINGS

2012 ◽  
Vol 12 (03) ◽  
pp. 1250179 ◽  
Author(s):  
A. AZIMI ◽  
A. ERFANIAN ◽  
M. FARROKHI D. G.
Keyword(s):  
Commutative Ring ◽  
Chromatic Number ◽  
Independence Number ◽  
Commutative Rings ◽  
Dominating Number ◽  
Jacobson Graph ◽  
Vertex Set ◽  
Numerical Invariants ◽  
Nonzero Identity

Let R be a commutative ring with nonzero identity. Then the Jacobson graph of R, denoted by 𝔍R, is defined as a graph with vertex set R\J(R) such that two distinct vertices x and y are adjacent if and only if 1 - xy is not a unit of R. We obtain some graph theoretical properties of 𝔍R including its connectivity, planarity and perfectness and we compute some of its numerical invariants, namely diameter, girth, dominating number, independence number and vertex chromatic number and give an estimate for its edge chromatic number.

scholarly journals Characterisation Results for Steiner Triple Systems and Their Application to Edge-Colourings of Cubic Graphs

2010 ◽  
Vol 62 (2) ◽  
pp. 355-381 ◽  
Author(s):  
Daniel Král’ ◽  
Edita Máčajov´ ◽  
Attila Pór ◽  
Jean-Sébastien Sereni
Keyword(s):  
Triple System ◽  
Steiner Triple System ◽  
Cubic Graphs ◽  
Steiner Triple Systems ◽  
Cubic Graph ◽  
Triple Systems ◽  
Forbidden Configurations ◽  
Edge Colourings

AbstractIt is known that a Steiner triple system is projective if and only if it does not contain the four-triple configuration C14. We find three configurations such that a Steiner triple system is affine if and only if it does not contain one of these configurations. Similarly, we characterise Hall triple systems using two forbidden configurations.Our characterisations have several interesting corollaries in the area of edge-colourings of graphs. A cubic graph G is S-edge-colourable for a Steiner triple system S if its edges can be coloured with points of S in such a way that the points assigned to three edges sharing a vertex form a triple in S. Among others, we show that all cubic graphs are S-edge-colourable for every non-projective nonaffine point-transitive Steiner triple system S.

scholarly journals On the Number of Spanning Trees in Random Regular Graphs

10.37236/3752 ◽  
2014 ◽  
Vol 21 (1) ◽  
Author(s):  
Catherine Greenhill ◽  
Matthew Kwan ◽  
David Wind
Keyword(s):  
Asymptotic Distribution ◽  
Regular Graph ◽  
Spanning Trees ◽  
Regular Graphs ◽  
Cubic Graph ◽  
Expected Number ◽  
Fixed Integer ◽  
Numerical Evidence ◽  
Number Of Spanning Trees

Let $d\geq 3$ be a fixed integer.   We give an asympotic formula for the expected number of spanning trees in a uniformly random $d$-regular graph with $n$ vertices. (The asymptotics are as $n\to\infty$, restricted to even $n$ if $d$ is odd.) We also obtain the asymptotic distribution of the number of spanning trees in a uniformly random cubic graph, and conjecture that the corresponding result holds for arbitrary (fixed) $d$. Numerical evidence is presented which supports our conjecture.

scholarly journals Smallest regular graphs without near 1-factors

1986 ◽  
Vol 41 (2) ◽  
pp. 193-210 ◽  
Author(s):  
Gary Chartrand ◽  
Sergio Ruiz ◽  
Curtiss E. Wall
Keyword(s):  
Regular Graph ◽  
Connected Graph ◽  
Regular Graphs ◽  
Cubic Graph ◽  
Subgraph Isomorphic ◽  
Even Order

AbstractA near 1-factor of a graph of order 2n ≧ 4 is a subgraph isomorphic to (n − 2) K2 ∪ P3 ∪ K1. Wallis determined, for each r ≥ 3, the order of a smallest r-regular graph of even order without a 1-factor; while for each r ≧ 3, Chartrand, Goldsmith and Schuster determined the order of a smallest r-regular, (r − 2)-edge-connected graph of even order without a 1-factor. These results are extended to graphs without near 1-factors. It is known that every connected, cubic graph with less than six bridges has a near 1-factor. The order of a smallest connected, cubic graph with exactly six bridges and no near 1-factor is determined.

scholarly journals A greedy algorithm for finding a large 2-matching on a random cubic graph

2017 ◽  
Vol 88 (3) ◽  
pp. 449-481
Author(s):  
Deepak Bal ◽  
Patrick Bennett ◽  
Tom Bohman ◽  
Alan Frieze
Keyword(s):  
Greedy Algorithm ◽  
Cubic Graph
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