Lower bounds on signed edge total domination numbers in graphs

Karami, H., Sheikholeslami, S. M., and Khodkar, Abdollah. "Lower bounds on signed edge total domination numbers in graphs." Czechoslovak Mathematical Journal 58.3 (2008): 595-603. <http://eudml.org/doc/37855>.

@article{Karami2008,
abstract = {The open neighborhood $N_G(e)$ of an edge $e$ in a graph $G$ is the set consisting of all edges having a common end-vertex with $e$. Let $f$ be a function on $E(G)$, the edge set of $G$, into the set $\lbrace -1, 1\rbrace $. If $ \sum _\{x\in N_G(e)\}f(x) \ge 1$ for each $e\in E(G)$, then $f$ is called a signed edge total dominating function of $G$. The minimum of the values $\sum _\{e\in E(G)\} f(e)$, taken over all signed edge total dominating function $f$ of $G$, is called the signed edge total domination number of $G$ and is denoted by $\gamma _\{st\}^\{\prime \}(G)$. Obviously, $\gamma _\{st\}^\{\prime \}(G)$ is defined only for graphs $G$ which have no connected components isomorphic to $K_2$. In this paper we present some lower bounds for $\gamma _\{st\}^\{\prime \}(G)$. In particular, we prove that $\gamma _\{st\}^\{\prime \}(T)\ge 2-m/3$ for every tree $T$ of size $m\ge 2$. We also classify all trees $T$ with $\gamma _\{st\}^\{\prime \}(T)=2-m/3$.},
author = {Karami, H., Sheikholeslami, S. M., Khodkar, Abdollah},
journal = {Czechoslovak Mathematical Journal},
keywords = {signed edge domination; signed edge total dominating function; signed edge total domination number; signed edge domination; signed edge total dominating function; signed edge total domination number},
language = {eng},
number = {3},
pages = {595-603},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Lower bounds on signed edge total domination numbers in graphs},
url = {http://eudml.org/doc/37855},
volume = {58},
year = {2008},
}

TY - JOUR
AU - Karami, H.
AU - Sheikholeslami, S. M.
AU - Khodkar, Abdollah
TI - Lower bounds on signed edge total domination numbers in graphs
JO - Czechoslovak Mathematical Journal
PY - 2008
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 58
IS - 3
SP - 595
EP - 603
AB - The open neighborhood $N_G(e)$ of an edge $e$ in a graph $G$ is the set consisting of all edges having a common end-vertex with $e$. Let $f$ be a function on $E(G)$, the edge set of $G$, into the set $\lbrace -1, 1\rbrace $. If $ \sum _{x\in N_G(e)}f(x) \ge 1$ for each $e\in E(G)$, then $f$ is called a signed edge total dominating function of $G$. The minimum of the values $\sum _{e\in E(G)} f(e)$, taken over all signed edge total dominating function $f$ of $G$, is called the signed edge total domination number of $G$ and is denoted by $\gamma _{st}^{\prime }(G)$. Obviously, $\gamma _{st}^{\prime }(G)$ is defined only for graphs $G$ which have no connected components isomorphic to $K_2$. In this paper we present some lower bounds for $\gamma _{st}^{\prime }(G)$. In particular, we prove that $\gamma _{st}^{\prime }(T)\ge 2-m/3$ for every tree $T$ of size $m\ge 2$. We also classify all trees $T$ with $\gamma _{st}^{\prime }(T)=2-m/3$.
LA - eng
KW - signed edge domination; signed edge total dominating function; signed edge total domination number; signed edge domination; signed edge total dominating function; signed edge total domination number
UR - http://eudml.org/doc/37855
ER -