# IJPAM: Volume 64, No. 3 (2010)

**UPPER MINUS DOMINATION NUMBER IN**

K-REGULAR GRAPHS

K-REGULAR GRAPHS

Hongtao Zhao, Xinzhong Lu

Department of Mathematics

Zhejiang Normal University

Jinhua, 321004, P.R. CHINA

e-mail: [email protected]

Department of Mathematics

Zhejiang Normal University

Jinhua, 321004, P.R. CHINA

e-mail: [email protected]

**Abstract.**Let be a graph. A function
defined on the the vertices of is a
minus domination function, if the sum of its function values over
any closed neighborhood is at least one. The weight of a minus
domination function is
. The upper
minus domination number of a graph , denoted ,
equals the maximum weight of all the minimal minus domination
functions of .

**Received: **October 25, 2010

**AMS Subject Classification: **26A33

**Key Words and Phrases: **minus domination, minus domination number, k-regular graph

**Source:** International Journal of Pure and Applied Mathematics

**ISSN:** 1311-8080

**Year:** 2010

**Volume:** 64

**Issue:** 3