Bounds on roman domination numbers of graphs

Roman dominating function of a graph G is a labeling function f : V (G) → {0, 1, 2} such that every vertex with label 0 has a neighbor with label 2. The Roman domination number R(G) of G is the minimum of Σv2V (G)f(v) over such functions. In this paper, we find lower and upper bounds for Roman domination numbers in terms of the diameter and the girth of G. .

[1]  Seyed Mahmoud Sheikholeslami,et al.  On the Roman domination number of a graph , 2009, Discret. Math..

[2]  Mathieu Liedloff,et al.  Roman Domination over Some Graph Classes , 2005, WG.

[3]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[4]  Erin W. Chambers,et al.  Extremal Problems for Roman Domination , 2009, SIAM J. Discret. Math..

[5]  Michael A. Henning,et al.  Defending the Roman Empire--A new strategy , 2003, Discret. Math..

[6]  Xin Chen,et al.  A note on Roman domination in graphs , 2006, Discret. Math..

[7]  Song,et al.  Roman Domination Number and Domination Number of a Tree , 2006 .

[8]  Michael A. Henning.  A characterization of Roman trees , 2002, Discuss. Math. Graph Theory.

[9]  Dieter Kratsch,et al.  Graph-Theoretic Concepts in Computer Science , 1987, Lecture Notes in Computer Science.

[10]  I. Stewart.  Defend the Roman Empire , 1999 .

[11]  Peter J. Slater,et al.  Fundamentals of domination in graphs , 1998, Pure and applied mathematics.

[12]  JH van Vuuren,et al.  Finite Order Domination in Graphs , 2003 .

[13]  Stephen T. Hedetniemi,et al.  Roman domination in graphs , 2004, Discret. Math..

[14]  Charles S. Revelle,et al.  Defendens Imperium Romanum: A Classical Problem in Military Strategy , 2000, Am. Math. Mon..

[15]  Michael A. Henning.  Defending the Roman Empire from multiple attacks , 2003, Discret. Math..