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pro vyhledávání: '"C., Susanth"'
Given a finite nonempty sequence $S$ of integers, write it as $XY^k$, consisting of a prefix $X$ (which may possibly be empty), followed by $k$ copies of a non-empty string $Y$. Then, the greatest such integer $k$ is called the curling number of $S$
Externí odkaz:
http://arxiv.org/abs/1512.01096
Given a finite nonempty sequence $S$ of integers, write it as $XY^k$, where $Y^k$ is a power of greatest exponent that is a suffix of $S$: this $k$ is the curling number of $S$. The concept of curling number of sequences has already been extended to
Externí odkaz:
http://arxiv.org/abs/1509.00220
We introduce the concept of a family of finite directed graphs (\emph{positive integer order,} $f(x) = mx + c; x,m \in \Bbb N$ and $c \in \Bbb N_0)$ which are directed graphs derived from an infinite directed graph called the $f(x)$-root digraph. The
Externí odkaz:
http://arxiv.org/abs/1506.06538
The bounds on the sum and product of chromatic numbers of a graph and its complement are known as Nordhaus-Gaddum inequalities. In this paper, we study the operations on the Independence numbers of graphs with their complement. We also provide a new
Externí odkaz:
http://arxiv.org/abs/1506.03251
The concept of the \emph{Gutman index}, denoted $Gut(G)$ was introduced for a connected undirected graph $G$. In this note we apply the concept to the underlying graphs of the family of Jaco graphs, (\emph{directed graphs by definition}), and describ
Externí odkaz:
http://arxiv.org/abs/1502.07093
Let $G^\rightarrow$ be a simple connected directed graph on $n \geq 2$ vertices and let $V^*$ be a non-empty subset of $V(G^\rightarrow)$ and denote the undirected subgraph induced by $V^*$ by, $\langle V^* \rangle.$ We show that the \emph{competitio
Externí odkaz:
http://arxiv.org/abs/1502.01824
The concept of the brush number $b_r(G)$ was introduced for a simple connected undirected graph $G$. The concept will be applied to the Mycielskian graph $\mu(G)$ of a simple connected graph $G$ to find $b_r(\mu(G))$ in terms of an \emph{optimal orie
Externí odkaz:
http://arxiv.org/abs/1501.03623
The concept of the brush number $b_r(G)$ was introduced for a simple connected undirected graph $G$. The concept will be applied to the Mycielski Jaco graph $\mu(J_n(1)), n \in \Bbb N,$ in respect of an \emph{optimal orientation} of $J_n(1)$ associat
Externí odkaz:
http://arxiv.org/abs/1501.01381
Autor:
Kok, Johan, C, Susanth
The concept of the \emph{McPherson number} of a simple connected graph $G$ on $n$ vertices denoted by $\Upsilon(G)$, is introduced. The recursive concept, called the \emph{McPherson recursion}, is a series of \emph{vertex explosions} such that on the
Externí odkaz:
http://arxiv.org/abs/1410.8637
Autor:
Kok, Johan, C, Susanth
Kok et.al. [7] introduced Jaco Graphs (\emph{order 1}). In this essay we present a recursive formula to determine the \emph{independence number} $\alpha(J_n(1)) = |\Bbb I|$ with, $\Bbb I = \{v_{i,j}| v_1 = v_{1,1} \in \Bbb I$ and $v_i = v_{i,j} =v_{(
Externí odkaz:
http://arxiv.org/abs/1410.8328