Relation Between Convexity Number and Independence Number of a Graph
نویسنده
چکیده
The convexity number denoted by in a connected graph is the maximum cardinality of a proper convex set in . Here in this paper graphs for which the independence number ( ) of a graph where ( ) = , ( ) < and ( ) > are completely characterised. Also graphs for which ( ) = are characterised. Construction of graphs with prescribed ( ) and are presented.
منابع مشابه
On relation between the Kirchhoff index and number of spanning trees of graph
Let $G=(V,E)$, $V={1,2,ldots,n}$, $E={e_1,e_2,ldots,e_m}$,be a simple connected graph, with sequence of vertex degrees$Delta =d_1geq d_2geqcdotsgeq d_n=delta >0$ and Laplacian eigenvalues$mu_1geq mu_2geqcdotsgeqmu_{n-1}>mu_n=0$. Denote by $Kf(G)=nsum_{i=1}^{n-1}frac{1}{mu_i}$ and $t=t(G)=frac 1n prod_{i=1}^{n-1} mu_i$ the Kirchhoff index and number of spanning tree...
متن کاملSOME GRAPH PARAMETERS ON THE COMPOSITE ORDER CAYLEY GRAPH
In this paper, the composite order Cayley graph Cay(G, S) is introduced, where G is a group and S is the set of all composite order elements of G. Some graph parameters such as diameter, girth, clique number, independence number, vertex chromatic number and domination number are calculated for the composite order Cayley graph of some certain groups. Moreover, the planarity of composite order Ca...
متن کاملINDEPENDENT SETS OF SOME GRAPHS ASSOCIATED TO COMMUTATIVE RINGS
Let $G=(V,E)$ be a simple graph. A set $Ssubseteq V$ isindependent set of $G$, if no two vertices of $S$ are adjacent.The independence number $alpha(G)$ is the size of a maximumindependent set in the graph. In this paper we study and characterize the independent sets ofthe zero-divisor graph $Gamma(R)$ and ideal-based zero-divisor graph $Gamma_I(R)$of a commutative ring $R$.
متن کاملComputing Multiplicative Zagreb Indices with Respect to Chromatic and Clique Numbers
The chromatic number of a graph G, denoted by χ(G), is the minimum number of colors such that G can be colored with these colors in such a way that no two adjacent vertices have the same color. A clique in a graph is a set of mutually adjacent vertices. The maximum size of a clique in a graph G is called the clique number of G. The Turán graph Tn(k) is a complete k-partite graph whose partition...
متن کاملGirth, minimum degree, independence, and broadcast independence
An independent broadcast on a connected graph $G$is a function $f:V(G)to mathbb{N}_0$such that, for every vertex $x$ of $G$, the value $f(x)$ is at most the eccentricity of $x$ in $G$,and $f(x)>0$ implies that $f(y)=0$ for every vertex $y$ of $G$ within distance at most $f(x)$ from $x$.The broadcast independence number $alpha_b(G)$ of $G$is the largest weight $sumlimits_{xin V(G)}f(x)$of an ind...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2014