scholarly journals ALGORITHMS FOR CONSTRUCTING EDGE MAGIC TOTAL LABELING OF COMPLETE BIPARTITE GRAPHS

2015 ◽  
pp. 55-58
Author(s):  
KRISHNAPPA H. K ◽  
N K. SRINATH ◽  
S. Manjunath ◽  
RAMAKANTH KUMAR P
Keyword(s):  
Bipartite Graph ◽  
Complete Bipartite Graph ◽  
Bipartite Graphs ◽  
Graph Labeling ◽  
Constant Independent ◽  
Magic Square ◽  
Complete Bipartite Graphs ◽  
One To One ◽  
Definition Of

The study of graph labeling has focused on finding classes of graphs which admits a particular type of labeling. In this paper we consider a particular class of graphs which demonstrates Edge Magic Total Labeling. The class we considered here is a complete bipartite graph Km,n. There are various graph labeling techniques that generalize the idea of a magic square has been proposed earlier. The definition of a magic labeling on a graph with v vertices and e edges is a one to one map taking the vertices and edges onto the integers 1,2,3,………, v+e with the property that the sum of the label on an edge and the labels of its endpoints is constant independent of the choice of edge. We use m x n matrix to construct edge magic total labeling of Km,n.

Rainbow Perfect Matchings in Complete Bipartite Graphs: Existence and Counting

2013 ◽  
Vol 22 (5) ◽  
pp. 783-799 ◽  
Author(s):  
GUILLEM PERARNAU ◽  
ORIOL SERRA
Keyword(s):  
Bipartite Graph ◽  
High Probability ◽  
Perfect Matching ◽  
Complete Bipartite Graph ◽  
Bipartite Graphs ◽  
Perfect Matchings ◽  
Asymptotic Enumeration ◽  
Complete Bipartite Graphs ◽  
Edge Colourings ◽  
Square Matrix

A perfect matchingMin an edge-coloured complete bipartite graphKn,nis rainbow if no pair of edges inMhave the same colour. We obtain asymptotic enumeration results for the number of rainbow perfect matchings in terms of the maximum number of occurrences of each colour. We also consider two natural models of random edge-colourings ofKn,nand show that if the number of colours is at leastn, then there is with high probability a rainbow perfect matching. This in particular shows that almost every square matrix of ordernin which every entry appearsntimes has a Latin transversal.

Finite locally-primitive complete bipartite graphs

2014 ◽  
Vol 17 (1) ◽  
Author(s):  
Wenwen Fan ◽  
Cai Heng Li ◽  
Jiangmin Pan
Keyword(s):  
Bipartite Graph ◽  
Complete Bipartite Graph ◽  
Bipartite Graphs ◽  
Complete Bipartite Graphs

Abstract.We characterize groups which act locally-primitively on a complete bipartite graph. The result particularly determines certain interesting factorizations of groups.

Note on T-Minimal Complete Bipartite Graphs

1968 ◽  
Vol 11 (5) ◽  
pp. 729-732 ◽  
Author(s):  
I. Z. Bouwer ◽  
I. Broere
Keyword(s):  
Natural Number ◽  
Bipartite Graph ◽  
Complete Bipartite Graph ◽  
Bipartite Graphs ◽  
Different Types ◽  
Complete Bipartite Graphs ◽  
Planar Subgraphs ◽  
Proper Subgraph

The thickness of a graph G is the smallest natural number t such that G is the union of t planar subgraphs. A graph G is t-minimal if its thickness is t and if every proper subgraph of G has thickness < t. (These terms were introduced by Tutte in [3]. In [1, p. 51] Beineke employs the term t-critical instead of t-minimal.) The complete bipartite graph K(m, n) consists of m 'dark1 points, n 'light' points, and the mn lines joining points of different types.

scholarly journals The IC-Indices of Complete Bipartite Graphs

10.37236/767 ◽  
2008 ◽  
Vol 15 (1) ◽  
Author(s):  
Chin-Lin Shiue ◽  
Hung-Lin Fu
Keyword(s):  
Bipartite Graph ◽  
Connected Graph ◽  
Complete Bipartite Graph ◽  
Bipartite Graphs ◽  
Connected Subgraph ◽  
Maximum Value ◽  
Complete Bipartite Graphs ◽  
Function Mapping

Let $G$ be a connected graph, and let $f$ be a function mapping $V(G)$ into ${\Bbb N}$. We define $f(H)=\sum_{v\in{V(H)}}f(v)$ for each subgraph $H$ of $G$. The function $f$ is called an IC-coloring of $G$ if for each integer $k$ in the set $\{1,2,\cdots,f(G)\}$ there exists an (induced) connected subgraph $H$ of $G$ such that $f(H)=k$, and the IC-index of $G$, $M(G)$, is the maximum value of $f(G)$ where $f$ is an IC-coloring of $G$. In this paper, we show that $M(K_{m,n})=3\cdot2^{m+n-2}-2^{m-2}+2$ for each complete bipartite graph $K_{m,n},\,2\leq m\leq n$.

scholarly journals Results on a Chromatic Number of a Bi-polar Fuzzy Complete Bipartite Graphs and Labelling of Tri-Polar Fuzzy Graphs

2021 ◽  
Vol 12 (2) ◽  
pp. 1040-1046
Author(s):  
Remala Mounika Lakshmi, Et. al.
Keyword(s):  
Bipartite Graph ◽  
Chromatic Number ◽  
Complete Bipartite Graph ◽  
Research Work ◽  
Bipartite Graphs ◽  
Network System ◽  
Route Network ◽  
Fuzzy Graphs ◽  
Complete Bipartite Graphs ◽  
Ultimate Objective

The ultimate objective of a piece of research work is to present the labelling of vertices in 3-PFG and labelling of distances in 3-PFG. Also, we characterize some of its properties. Later, we define the vertex and edge chromatic number BF- Complete Bipartite graph. Further we illustrated an example for BFRGS which represents a Route Network system.

scholarly journals A Quantitative Approach to Perfect One-Factorizations of Complete Bipartite Graphs

10.37236/4122 ◽  
2015 ◽  
Vol 22 (1) ◽  
Author(s):  
Natacha Astromujoff ◽  
Martin Matamala
Keyword(s):  
Bipartite Graph ◽  
Complete Bipartite Graph ◽  
Bipartite Graphs ◽  
Perfect Matchings ◽  
Quantitative Approach ◽  
Hamiltonian Cycles ◽  
Complete Bipartite Graphs

Given a one-factorization $\mathcal{F}$ of the complete bipartite graph $K_{n,n}$, let ${\sf pf}(\mathcal{F})$ denote the number of Hamiltonian cycles obtained by taking pairwise unions of perfect matchings in $\mathcal{F}$. Let ${\sf pf}(n)$ be the maximum of ${\sf pf}(\mathcal{F})$ over all one-factorizations $\mathcal{F}$ of $K_{n,n}$. In this work we prove that ${\sf pf}(n)\geq n^2/4$, for all $n\geq 2$.

ON PROBLEMS OF -CONNECTED GRAPHS FOR

2020 ◽  
pp. 1-8
Author(s):  
MICHAL STAŠ ◽  
JURAJ VALISKA
Keyword(s):  
Bipartite Graph ◽  
Connected Graph ◽  
Complete Bipartite Graph ◽  
Bipartite Graphs ◽  
Connected Graphs ◽  
Complete Bipartite Graphs

Abstract A connected graph G is $\mathcal {CF}$ -connected if there is a path between every pair of vertices with no crossing on its edges for each optimal drawing of G. We conjecture that a complete bipartite graph $K_{m,n}$ is $\mathcal {CF}$ -connected if and only if it does not contain a subgraph of $K_{3,6}$ or $K_{4,4}$ . We establish the validity of this conjecture for all complete bipartite graphs $K_{m,n}$ for any $m,n$ with $\min \{m,n\}\leq 6$ , and conditionally for $m,n\geq 7$ on the assumption of Zarankiewicz’s conjecture that $\mathrm {cr}(K_{m,n})=\big \lfloor \frac {m}{2} \big \rfloor \big \lfloor \frac {m-1}{2} \big \rfloor \big \lfloor \frac {n}{2} \big \rfloor \big \lfloor \frac {n-1}{2} \big \rfloor $ .

scholarly journals Note on Path-Connectivity of Complete Bipartite Graphs

2021 ◽  
pp. 2142014
Author(s):  
Xiaoxue Gao ◽  
Shasha Li ◽  
Yan Zhao
Keyword(s):  
Bipartite Graph ◽  
Complete Bipartite Graph ◽  
Discrete Math ◽  
Bipartite Graphs ◽  
Complete Bipartite Graphs

For a graph [Formula: see text] and a set [Formula: see text] of size at least [Formula: see text], a path in [Formula: see text] is said to be an [Formula: see text]-path if it connects all vertices of [Formula: see text]. Two [Formula: see text]-paths [Formula: see text] and [Formula: see text] are said to be internally disjoint if [Formula: see text] and [Formula: see text]. Let [Formula: see text] denote the maximum number of internally disjoint [Formula: see text]-paths in [Formula: see text]. The [Formula: see text]-path-connectivity [Formula: see text] of [Formula: see text] is then defined as the minimum [Formula: see text], where [Formula: see text] ranges over all [Formula: see text]-subsets of [Formula: see text]. In [M. Hager, Path-connectivity in graphs, Discrete Math. 59 (1986) 53–59], the [Formula: see text]-path-connectivity of the complete bipartite graph [Formula: see text] was calculated, where [Formula: see text]. But, from his proof, only the case that [Formula: see text] was considered. In this paper, we calculate the situation that [Formula: see text] and complete the result.

Sign in / Sign up

Export Citation Format

Share Document