The Binding Number of a Digraph

2007 ◽  
pp. 221-227
Author(s):  
Genjiu Xu ◽  
Xueliang Li ◽  
Shenggui Zhang
Keyword(s):  
Binding Number

Binding Number, Minimum Degree, and Cycle Structure in Graphs

2012 ◽  
Vol 71 (2) ◽  
pp. 219-228 ◽  
Author(s):  
D. Bauer ◽  
E. Schmeichel
Keyword(s):  
Minimum Degree ◽  
Cycle Structure ◽  
Binding Number

scholarly journals Best monotone degree conditions for binding number

2011 ◽  
Vol 311 (18-19) ◽  
pp. 2037-2043 ◽  
Author(s):  
D. Bauer ◽  
M. Yatauro ◽  
N. Kahl ◽  
E. Schmeichel
Keyword(s):  
Binding Number ◽  
Degree Conditions

A New Sufficient Condition for a Graph To Be (g, f, n)-Critical

2010 ◽  
Vol 53 (2) ◽  
pp. 378-384
Author(s):  
Sizhong Zhou
Keyword(s):  
Sufficient Condition ◽  
Binding Number ◽  
Minimum Value ◽  
Spanning Subgraph ◽  
Critical Graph

AbstractLet G be a graph of order p, let a, b, and n be nonnegative integers with 1 ≤ a < b, and let g and f be two integer-valued functions defined on V(G) such that a ≤ g(x) < f (x) ≤ b for all x ∈ V(G). A (g, f )-factor of graph G is a spanning subgraph F of G such that g(x) ≤ dF(x) ≤ f (x) for each x ∈ V(F). Then a graph G is called (g, f, n)-critical if after deleting any n vertices of G the remaining graph of G has a (g, f )-factor. The binding number bind(G) of G is the minimum value of |NG(X)|/|X| taken over all non-empty subsets X of V(G) such that NG(X) ≠ V(G). In this paper, it is proved that G is a (g, f, n)-critical graph ifFurthermore, it is shown that this result is best possible in some sense.

The binding number of product graphs

1984 ◽  
pp. 119-128 ◽  
Author(s):  
Wang Jianfang ◽  
Tian Songlin ◽  
Liu Jiuqiang
Keyword(s):  
Binding Number ◽  
Product Graphs

scholarly journals A parameter linked with G-factors and the binding number

1991 ◽  
Vol 91 (3) ◽  
pp. 311-316 ◽  
Author(s):  
O. Favaron ◽  
M.C. Heydemann ◽  
J.C. Meyer ◽  
D. Sotteau
Keyword(s):  
Binding Number ◽  
G Factors

scholarly journals Toughness, binding number and restricted matching extension in a graph

2017 ◽  
Vol 340 (11) ◽  
pp. 2665-2672 ◽  
Author(s):  
Michael D. Plummer ◽  
Akira Saito
Keyword(s):  
Binding Number

A result on fractional $k$-deleted graphs

2010 ◽  
Vol 106 (1) ◽  
pp. 99 ◽  
Author(s):  
Sizhong Zhou
Keyword(s):  
Binding Number ◽  
K Factor

Let $k\geq 2$ be an integer, and let $G$ be a graph of order $n$ with $n\geq4k-5$. A graph $G$ is a fractional $k$-deleted graph if there exists a fractional $k$-factor after deleting any edge of $G$. The binding number of $G$ is defined as 26741 {\operatorname {bind}} (G)=\min\left\{\frac{|N_G(X)|}{|X|}:\emptyset\neq X\subseteq V(G),N_G(X)\neq V(G)\right\}. 26741 In this paper, it is proved that if ${\operatorname {bind}} (G)>\frac{(2k-1)(n-1)}{k(n-2)}$, then $G$ is a fractional $k$-deleted graph. Furthermore, it is shown that the result in this paper is best possible in some sense.

Binding Number and Wheel Related Graphs

2017 ◽  
Vol 28 (01) ◽  
pp. 29-38 ◽  
Author(s):  
Vecdi Aytaç ◽  
Zeynep Nihan Berberler
Keyword(s):  
Characteristic Quantity ◽  
Binding Number

The binding number of a graph G is defined to be the minimum of [Formula: see text] taken over all nonempty [Formula: see text] such that [Formula: see text]. Binding number, one indicator to better understand graph, is an important characteristic quantity of a graph. In this paper, the relationships between the binding number and some other graph vulnerability parameters, namely the toughness, integrity, rupture degree and scattering number, are established. Exact values for the binding numbers of wheel related graphs namely gear, helm, sunflower and friendship graph are obtained.

A Binding Number Computation of Graph

2008 ◽  
Author(s):  
Congying Han ◽  
Guoping He ◽  
Hua Duan ◽  
Xuping Zhang
Keyword(s):  
Binding Number
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