scholarly journals Special Classes of Coprime Irregular Graphs

2020 ◽  
pp. 269-271
Keyword(s):  
Positive Integer ◽  
Edge Weighting ◽  
Irregular Graphs ◽  
Special Classes

: An k-edge-weighting of a graph G = (V, E) is a mapping : E(G) {1, 2, 3, ...k}, where k is a positive integer. The sum of the edge-weighting appearing on the edges incident at the vertex v under the edge-weighting and is denoted by (v). An k edge-weighting of G is a coprime irregular edge-weighting if gcd ( (u), (v)) = 1 for every pair of adjacent vertices u and v in G. A graph G admits a coprime irregular edge-weighting is called a coprime irregular graph. In this paper, we discuss the coprime irregular edge-weighting for some special classes of graphs.

scholarly journals On Equitable Irregular Graphs

2020 ◽  
Vol 8 (4S4) ◽  
pp. 122-124
Keyword(s):  
Positive Integer ◽  
Edge Weighting ◽  
Irregular Graphs

An k−edge-weighting of a graph G = (V,E) is a map 𝝋: 𝑬(𝑮) → {𝟏,𝟐,𝟑, . . . 𝒌}, }where 𝒌 ≥ 𝟏 is an integer. Denote 𝑺𝝋(𝒗) is the sum of edge-weights appearing on the edges incident at the vertex v under𝝋 . An k-edge -weighting of G is equitable irregular if |𝑺𝝋(𝒖) − 𝑺𝝋(𝒗)| ≤ 𝟏, for every pair of adjacent vertices u and v in G. The equitable irregular strength 𝑺𝒆 (𝑮) of an equitable irregular graph G is the smallest positive integer k such that there is a k-edge weighting of G. In this paper, we discuss the equitable irregular edge-weighting for some classes of graphs

scholarly journals Coprime Irregular graphs

2019 ◽  
Vol 9 (1S4) ◽  
pp. 1093-1096
Keyword(s):  
Positive Integer ◽  
Edge Weighting ◽  
Irregular Graphs

An l-edge-weighting of a graph G is a map : E(G) {1, 2, 3, … l}, where l is a positive integer. For a vertex v V(G), the weight (v) is the sum of edge-weights appearing on the edges incident at v under the edge-weighting . An l-edge-weighting of G is coprime irregular edge-weighting of G if gcd( (u), (v)) = 1 for every pair of adjacent vertices u and v in G. A graph G is coprime irregular if G admits a coprime irregular edge-weighting. In this paper, we discuss this new irregular edge weighting of graphs.

scholarly journals More on Coprime Irregular Graphs

2019 ◽  
Vol 9 (1S4) ◽  
pp. 1014-1016
Keyword(s):  
Positive Integer ◽  
Edge Weighting ◽  
Irregular Graphs

An k−edge-weighting of a graph G = (V,E) is a map φ: E(G) → {1,2,3,...k}, where k is a positive integer. Denote Sφ(v) is the sum of edge-weights presenting on the edges incident at the vertex v under the edge-weighting φ. An k−edge-weighting of G is coprime irregular edge-weighting of G if gcd(Sφ(u),Sφ(v)) = 1 for every pair of adjacent vertices u and v in G. A graph G is coprime irregular if G admits a coprime irregular edge-weighting. In this paper, we discuss about coprime irregular edge-weighting for some families of graphs

The Order of Monochromatic Subgraphs with a Given Minimum Degree

10.37236/1725 ◽  
2003 ◽  
Vol 10 (1) ◽  
Author(s):  
Yair Caro ◽  
Raphael Yuster
Keyword(s):  
Positive Integer ◽  
Minimum Degree

Let $G$ be a graph. For a given positive integer $d$, let $f_G(d)$ denote the largest integer $t$ such that in every coloring of the edges of $G$ with two colors there is a monochromatic subgraph with minimum degree at least $d$ and order at least $t$. Let $f_G(d)=0$ in case there is a $2$-coloring of the edges of $G$ with no such monochromatic subgraph. Let $f(n,k,d)$ denote the minimum of $f_G(d)$ where $G$ ranges over all graphs with $n$ vertices and minimum degree at least $k$. In this paper we establish $f(n,k,d)$ whenever $k$ or $n-k$ are fixed, and $n$ is sufficiently large. We also consider the case where more than two colors are allowed.

Improving Color Constancy by Photometric Edge Weighting

2012 ◽  
Vol 34 (5) ◽  
pp. 918-929 ◽  
Author(s):  
A. Gijsenij ◽  
T. Gevers ◽  
J. van de Weijer
Keyword(s):  
Color Constancy ◽  
Edge Weighting
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