Weak signed total Italian domination in graphs

Articles in Press

Document Type : Original paper

Author

RWTH Aachen University

Abstract

A {\em weak signed total Italian dominating function} (WSTIDF) of a graph

G

with vertex set

V (G)

is defined as a
function

f : V (G) \to {- 1, 1, 2}

having the property that

\sum_{x \in N (v)} f (x) \geq 1

for each

v \in V (G)

, where

N (v)

is the
neighborhood of

v

. The weight of a WSTIDF is the sum of its function values over all vertices.
The {\em weak signed total Italian domination number} of

G

, denoted by

γ_{w s t I} (G)

, is the minimum weight of a WSTIDF in

G

.
We initiate the study of the weak signed total Italian domination number, and we present different sharp bounds on

γ_{w s t I} (G)

.
In addition, we determine the weak signed total Italian domination number of some classes of graphs.

Keywords

Main Subjects