scholarly journals Fuzzy square difference labeling of some graphs

10.26524/cm93 ◽  
2021 ◽  
Vol 5 (1) ◽  
Author(s):  
Bharathi T ◽  
Jeya Rowena ◽  
Ashwini Sibiya Rani P
Keyword(s):  
Bipartite Graph ◽  
Complete Bipartite Graph ◽  
Star Graph ◽  
Path Graph ◽  
Difference Graphs ◽  
Cycle Graph

We introduced a new concept called the Fuzzy square difference labeling. We proved that the path graph (Pn), the cycle graph (Cn), the star graph (Sn) and the complete bipartite graph (Km,n, n ≤ 3) are Fuzzy square difference graphs.

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.

6. Graphs

2016 ◽  
pp. 86-108
Author(s):  
Robin Wilson
Keyword(s):  
Graph Theory ◽  
Bipartite Graph ◽  
Complete Graph ◽  
Planar Graphs ◽  
Complete Bipartite Graph ◽  
Travelling Salesman Problem ◽  
Chemical Bonds ◽  
Hamiltonian Graphs ◽  
Road Map ◽  
Cycle Graph

Graph theory is about collections of points that are joined in pairs, such as a road map with towns connected by roads or a molecule with atoms joined by chemical bonds. ‘Graphs’ revisits the Königsberg bridges problem, the knight’s tour problem, the Gas–Water–Electricity problem, the map-colour problem, the minimum connector problem, and the travelling salesman problem and explains how they can all be considered as problems in graph theory. It begins with an explanation of a graph and describes the complete graph, the complete bipartite graph, and the cycle graph, which are all simple graphs. It goes on to describe trees in graph theory, Eulerian and Hamiltonian graphs, and planar graphs.

scholarly journals DIMENSI METRIK KETETANGGAAN LOKAL GRAF HASIL OPERASI k-COMB

2019 ◽  
Vol 1 (1) ◽  
pp. 1
Author(s):  
Fryda Arum Pratama ◽  
Liliek Susilowati ◽  
Moh. Imam Utoyo
Keyword(s):  
Complete Graph ◽  
Connected Graph ◽  
Metric Dimension ◽  
Star Graph ◽  
K Value ◽  
Product Graph ◽  
Path Graph ◽  
Dominating Number ◽  
Cycle Graph

Research on the local adjacency metric dimension has not been found in all operations of the graph, one of them is comb product graph. The purpose of this research was to determine the local adjacency metric dimension of k-comb product graph and level  comb product graph between any connected graph G and H. In this research graph G and graph H such as cycle graph, complete graph, path graph, and star graph. K-comb product graph between any graph G and H denoted by GokH. While level k comb product graph between any graph G and H denoted by GokH.In this research, local adjacency metric dimension of GokSm graph only dependent to multiplication of the cardinality of V(G) and many of k value, while GokKm graph and GokCm graph is dependent to dominating number of G and multiplication of the cardinality of V(G), many of k value, and local adjacency metric dimension of Km graph or Cm graph. And then, local adjacency metric dimension of GokSm graph only dependent to the cardinality of V(Gok-1Sm), while GokKm graph and GokCm graph is dependent to dominating number of G and multiplication of the local adjacency metric dimension of Km graph or Cm graph with cardinality of V(Gok-1Km) or V(Gok-1Cm). 

A neigborhood union condition for nonadjacent vertices in graphs

2017 ◽  
Vol 09 (05) ◽  
pp. 1750060
Author(s):  
Farzad Shaveisi
Keyword(s):  
Bipartite Graph ◽  
Complete Bipartite Graph ◽  
Simple Graph ◽  
Strongly Regular Graphs ◽  
Star Graph ◽  
Regular Graphs ◽  
Strongly Regular ◽  
Union Condition ◽  
Bounded Graph

A simple graph [Formula: see text] is called [Formula: see text]-bounded if for every two nonadjacent vertices [Formula: see text] of [Formula: see text] there exists a vertex [Formula: see text] such that [Formula: see text], where [Formula: see text] denotes the set of neighbors of the vertex [Formula: see text] in [Formula: see text]. In this paper, some properties of [Formula: see text]-bounded graphs are studied. It is shown that any bipartite [Formula: see text]-bounded graph is a complete bipartite graph with at most two horns; in particular, any [Formula: see text]-bounded tree is either a star or a two-star graph. Also, we prove that any non-end vertex of every [Formula: see text]-bounded graph is contained in either a triangle or a rectangle. Among other results, it is shown that all regular [Formula: see text]-bounded graphs are strongly regular graphs. Finally, we determine that how many edges can an [Formula: see text]-bounded graph have?

scholarly journals b-CHROMATIC NUMBER OF CORONA PRODUCT OF CROWN GRAPH AND COMPLETE BIPARTITE GRAPH WITH PATH GRAPH

2015 ◽  
Vol 2 (2) ◽  
pp. 30-33
Author(s):  
Vijayalakshmi D ◽  
Mohanappriya G
Keyword(s):  
Bipartite Graph ◽  
Structural Properties ◽  
Chromatic Number ◽  
Complete Bipartite Graph ◽  
Proper Coloring ◽  
Path Graph ◽  
Crown Graph ◽  
Corona Product

A b-coloring of a graph is a proper coloring where each color admits at least one node (called dominating node) adjacent to every other used color. The maximum number of colors needed to b-color a graph G is called the b-chromatic number and is denoted by φ(G). In this paper, we find the b-chromatic number and some of the structural properties of corona product of crown graph and complete bipartite graphwith path graph.

scholarly journals Duplicating a Vertex with an Edge in Divided Square Difference Cordial Graphs

2018 ◽  
Vol 7 (1) ◽  
pp. 1-8
Author(s):  
A. Alfred Leo ◽  
R Vikramaprasad
Keyword(s):  
Star Graph ◽  
Path Graph ◽  
Wheel Graph ◽  
Crown Graph ◽  
Cycle Graph

In this present work, we discuss divided square difference (DSD) cordial labeling in the context of duplicating a vertex with an edge in DSD cordial graphs such as path graph, cycle graph, star graph, wheel graph, helm graph, crown graph, comb graph and snake graph.

Betti number of nilpotent Lie algebras and graph ideals

2015 ◽  
Vol 08 (03) ◽  
pp. 1550046
Author(s):  
Ahmad Khaksari
Keyword(s):  
Spectral Sequence ◽  
Bipartite Graph ◽  
Lie Algebras ◽  
Betti Number ◽  
Complete Bipartite Graph ◽  
Betti Numbers ◽  
Heisenberg Algebra ◽  
Star Graph ◽  
Nilpotent Lie Algebras ◽  
One Dimensional

It is shown that, how spectral sequence arguments can contribute to a solution in a concrete setting. For one-dimensional extensions of a Heisenberg algebra, we determine the Betti numbers exactly and then show that some families in this class have a M-shaped Betti number distribution, and construct the first examples with an even more exotic complete bipartite graph which are independent of choice of field. Finally, we discuss the Betti numbers for the star graph with [Formula: see text] vertices.

Graceful Labeling for Some Complete Bipartite Graph

2018 ◽  
Vol 9 (12) ◽  
pp. 2147-2152
Author(s):  
V. Raju ◽  
M. Paruvatha vathana
Keyword(s):  
Bipartite Graph ◽  
Complete Bipartite Graph ◽  
Graceful Labeling

On the Crossing Number of $K_{m,n}$

10.37236/1748 ◽  
2003 ◽  
Vol 10 (1) ◽  
Author(s):  
Nagi H. Nahas
Keyword(s):  
Lower Bound ◽  
Bipartite Graph ◽  
Complete Bipartite Graph ◽  
Crossing Number

The best lower bound known on the crossing number of the complete bipartite graph is : $$cr(K_{m,n}) \geq (1/5)(m)(m-1)\lfloor n/2 \rfloor \lfloor(n-1)/2\rfloor$$ In this paper we prove that: $$cr(K_{m,n}) \geq (1/5)m(m-1)\lfloor n/2 \rfloor \lfloor (n-1)/2 \rfloor + 9.9 \times 10^{-6} m^2n^2$$ for sufficiently large $m$ and $n$.

Packing coloring on subdivision-vertex and subdivision-edge join of cycle Cm with path Pn

2020 ◽  
pp. 627-634
Author(s):  
K. Rajalakshmi ◽  
M. Venkatachalam ◽  
M. Barani ◽  
D. Dafik
Keyword(s):  
Chromatic Number ◽  
Path Graph ◽  
Packing Chromatic Number ◽  
Cycle Graph

The packing chromatic number $\chi_\rho$ of a graph $G$ is the smallest integer $k$ for which there exists a mapping $\pi$ from $V(G)$ to $\{1,2,...,k\}$ such that any two vertices of color $i$ are at distance at least $i+1$. In this paper, the authors find the packing chromatic number of subdivision vertex join of cycle graph with path graph and subdivision edge join of cycle graph with path graph.

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