the common minimal dominating signed graph
Authors
abstract
in this paper, we define the common minimal dominating signed graph of a given signed graph and offer a structural characterization of common minimal dominating signed graphs. in the sequel, we also obtained switching equivalence characterizations: $overline{s} sim cmd(s)$ and $cmd(s) sim n(s)$, where $overline{s}$, $cmd(s)$ and $n(s)$ are complementary signed graph, common minimal signed graph and neighborhood signed graph of $s$ respectively.
similar resources
the common minimal common neighborhood dominating signed graphs
in this paper, we define the common minimal common neighborhooddominating signed graph (or common minimal $cn$-dominating signedgraph) of a given signed graph and offer a structuralcharacterization of common minimal $cn$-dominating signed graphs.in the sequel, we also obtained switching equivalencecharacterization: $overline{sigma} sim cmcn(sigma)$, where$overline{sigma}$ and $cmcn(sigma)$ are ...
full textVertex Minimal and Common Minimal Equitable Dominating Graphs
In this paper we introduce the common minimal equitable and vertex minimal equitable dominating graph and we get characterize the common minimal equitable and vertex minimal equitable dominating graph which are either connected or complete, some new results of these graphs are obtained. Mathematics Subject Classification: 05C70
full textSigned Dominating and Total Dominating Functions of Corona Product Graph of a Path with a Star
Domination in graphs has been an extensively researched branch of graph theory. Graph theory is one of the most flourishing branches of modern mathematics and computer applications. An introduction and an extensive overview on domination in graphs and related topics is surveyed and detailed in the two books by Haynes et al. [ 1, 2]. Recently dominating functions in domination theory have receiv...
full textminimal, vertex minimal and commonality minimal cn-dominating graphs
we define minimal cn-dominating graph $mathbf {mcn}(g)$, commonality minimal cn-dominating graph $mathbf {cmcn}(g)$ and vertex minimal cn-dominating graph $mathbf {m_{v}cn}(g)$, characterizations are given for graph $g$ for which the newly defined graphs are connected. further serval new results are developed relating to these graphs.
full textMinimal Dominating Sets in Graph Classes: Combinatorial Bounds and Enumeration
The maximum number of minimal dominating sets that a graph on n vertices can have is known to be at most 1.7159. This upper bound might not be tight, since no examples of graphs with 1.5705 or more minimal dominating sets are known. For several classes of graphs, we substantially improve the upper bound on the maximum number of minimal dominating sets in graphs on n vertices. In some cases, we ...
full textThe H - Line Signed Graph of a Signed Graph
A Smarandachely k-signed graph (Smarandachely k-marked graph) is an ordered pair S = (G,σ) (S = (G,μ)) where G = (V, E) is a graph called underlying graph of S and σ : E → (e1, e2, ..., ek) (μ : V → (e1, e2, ..., ek)) is a function, where each ei ∈ {+,−}. Particularly, a Smarandachely 2-signed graph or Smarandachely 2-marked graph is called abbreviated a signed graph or a marked graph. Given a ...
full textMy Resources
Save resource for easier access later
Journal title:
transactions on combinatoricsPublisher: university of isfahan
ISSN 2251-8657
volume 1
issue 3 2012
Hosted on Doprax cloud platform doprax.com
copyright © 2015-2023