منابع مشابه
On the Number of Resolving Pairs in Graphs
Let G be a connected graph. An unordered pair {x, y} of vertices of G is a resolving pair if no vertex of G has the same distance to x and y. It was conjectured in [8] that the number of resolving pairs of a connected graph of order n is bounded above by bn2 4 c. In this note we show that there exists a constant c > 0 such that for sufficiently large n every graph of order n contains at most ( ...
متن کاملOn the fixed number of graphs
A set of vertices $S$ of a graph $G$ is called a fixing set of $G$, if only the trivial automorphism of $G$ fixes every vertex in $S$. The fixing number of a graph is the smallest cardinality of a fixing set. The fixed number of a graph $G$ is the minimum $k$, such that every $k$-set of vertices of $G$ is a fixing set of $G$. A graph $G$ is called a $k$-fixed graph, if its fix...
متن کاملOn the saturation number of graphs
Let $G=(V,E)$ be a simple connected graph. A matching $M$ in a graph $G$ is a collection of edges of $G$ such that no two edges from $M$ share a vertex. A matching $M$ is maximal if it cannot be extended to a larger matching in $G$. The cardinality of any smallest maximal matching in $G$ is the saturation number of $G$ and is denoted by $s(G)$. In this paper we study the saturation numbe...
متن کاملOn the super domination number of graphs
The open neighborhood of a vertex $v$ of a graph $G$ is the set $N(v)$ consisting of all vertices adjacent to $v$ in $G$. For $Dsubseteq V(G)$, we define $overline{D}=V(G)setminus D$. A set $Dsubseteq V(G)$ is called a super dominating set of $G$ if for every vertex $uin overline{D}$, there exists $vin D$ such that $N(v)cap overline{D}={u}$. The super domination number of $G$ is the minimum car...
متن کاملOn the Average Number of Edges in Theta Graphs
Theta graphs are important geometric graphs that have many applications, including wireless networking, motion planning, real-time animation, and minimumspanning tree construction. We give closed form expressions for the average degree of theta graphs of a homogeneous Poisson point process over the plane. We then show that essentially the same bounds—with vanishing error terms—hold for theta gr...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: International Journal of Future Generation Communication and Networking
سال: 2019
ISSN: 2233-7857,2207-9645
DOI: 10.33832/ijfgcn.2019.12.4.03