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On Signed Star Domination in Graphs

On Signed Star Domination in Graphs For a graph G = (V, E) without isolated vertex, a function f: E(G) → {−1, 1} is said to be a signed star dominating function of G $$\sum\limits_{e \in E(v)} {f(e) \ge 1} $$ for every v ∈ V(G), where E(v) = {uv} ∈ E(G)∣ u ∈ V(G)}. The minimum value of $$\sum\limits_{e \in E(G)} {f(e)} $$ , taken over all signed star dominating functions f of G, is called the signed star domination number of G and is denoted by γss(G). This paper studies the bounds and algorithms of signed star domination numbers in some classes of graphs. In particular, sharp bounds for the signed star domination number of a general graph and a linear-time algorithm for the signed star domination problem in a tree is presented. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

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Publisher
Springer Journals
Copyright
Copyright © 2019 by The Editorial Office of AMAS & Springer-Verlag GmbH Germany
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/s10255-019-0816-8
Publisher site
See Article on Publisher Site

Abstract

For a graph G = (V, E) without isolated vertex, a function f: E(G) → {−1, 1} is said to be a signed star dominating function of G $$\sum\limits_{e \in E(v)} {f(e) \ge 1} $$ for every v ∈ V(G), where E(v) = {uv} ∈ E(G)∣ u ∈ V(G)}. The minimum value of $$\sum\limits_{e \in E(G)} {f(e)} $$ , taken over all signed star dominating functions f of G, is called the signed star domination number of G and is denoted by γss(G). This paper studies the bounds and algorithms of signed star domination numbers in some classes of graphs. In particular, sharp bounds for the signed star domination number of a general graph and a linear-time algorithm for the signed star domination problem in a tree is presented.

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: May 15, 2019

References