Discussiones Mathematicae Graph Theory, Volume (39), No (1), Year (2019-2) , Pages (841-856)

#### Title : ( ON INDEPENDENT DOMINATION IN PLANAR, CUBIC GRAPHS )

Authors: Freydoon Rahbarnia ,

Citation: BibTeX | EndNote

#### Abstract

A set S of vertices in a graph G is an independent dominating set of G if S is an independent set and every vertex not in S is adjacent to a vertex in S. The independent domination number, i(G), of G is the minimum cardinality of an independent dominating set. Goddard and Henning [Discrete Math. 313 (2013) 839–854] posed the conjecture that if G /∈ {K3,3,C5 K2} is a connected, cubic graph on n vertices, then i(G) ≤ 3 8n, where C5 K2 is the 5-prism. As an application of known result, we observe that this conjecture is true when G is 2-connected and planar, and we provide an infinite family of such graphs that achieve the bound. We conjecture that if G is a bipartite, planar, cubic graph of order n, then i(G) ≤ 1 3n, and we provide an infinite family of such graphs that achieve this bound.

#### Keywords

, independent domination number, domination number, cubic graphs.
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@article{paperid:1070741,
author = {Rahbarnia, Freydoon},
title = {ON INDEPENDENT DOMINATION IN PLANAR, CUBIC GRAPHS},
journal = {Discussiones Mathematicae Graph Theory},
year = {2019},
volume = {39},
number = {1},
month = {February},
issn = {1234-3099},
pages = {841--856},
numpages = {15},
keywords = {independent domination number; domination number; cubic graphs.},
}

%0 Journal Article
%T ON INDEPENDENT DOMINATION IN PLANAR, CUBIC GRAPHS
%A Rahbarnia, Freydoon
%J Discussiones Mathematicae Graph Theory
%@ 1234-3099
%D 2019