.Dara Moazzami
Abstract
The edge-tenacity $T_e(G)$ of a graph G was defined as\begin{center} $T_e(G)=\displaystyle \min_{F\subset E(G)}\{\frac{\mid F\mid +\tau(G-F)}{\omega(G-F)}\}$\end{center}where the minimum is taken over all edge cutset F of G. We defineG-F to be the graph induced by the edges of $E(G)-F$, $\tau(G-F)$is ...
Read More
The edge-tenacity $T_e(G)$ of a graph G was defined as\begin{center} $T_e(G)=\displaystyle \min_{F\subset E(G)}\{\frac{\mid F\mid +\tau(G-F)}{\omega(G-F)}\}$\end{center}where the minimum is taken over all edge cutset F of G. We defineG-F to be the graph induced by the edges of $E(G)-F$, $\tau(G-F)$is the number of edges in the largest component of the graphinduced by G-F and $\omega(G-F)$ is the number of components of$G-F$. A set $F\subset E(G)$ is said to be a $T_e$-set of G if\begin{center} $T_e(G)=\frac{\mid F\mid+\tau(G-F)}{\omega(G-F)}$\end{center}Each component has at least one edge. In this paper we introducea new invariant edge-tenacity, for graphs. it is another vulnerability measure.we present several properties and bounds on the edge-tenacity. we alsocompute the edge-tenacity of some classes of graphs.
Dara Moazzami
Abstract
Numerous networks as, for example, road networks, electrical networks and communication networks can be modeled by a graph. Many attempts have been made to determine how well such a network is "connected" or stated differently how much effort is required to break down communication in the system between ...
Read More
Numerous networks as, for example, road networks, electrical networks and communication networks can be modeled by a graph. Many attempts have been made to determine how well such a network is "connected" or stated differently how much effort is required to break down communication in the system between at least some nodes. Two well-known measures that indicate how "reliable" a graph is are the "Tenacity" and "Edge-tenacity" of a graph. In this paper we present results on the tenacity and edge-tenacity, $T_e(G)$, a new invariant, for several classes of graphs. Basic properties and some bounds for edge-tenacity, $T_e(G)$, are developed. Edge-tenacity values for various classes of graphs are calculated and future work andconcluding remarks are summarized
