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Counting independent sets of a fixed size in graphs with a given minimum degree
graphs given minimum degree independent sets Combinatorics
2012/4/16
Galvin showed that for all fixed $\delta$ and sufficiently large $n$, the $n$-vertex graph with minimum degree $\delta$ that admits the most independent sets is the complete bipartite graph $K_{\delta...
Normality of the three-state toric homogeneous Markov chain model
Markov bases toric homogeneous Markov chains polyhedrons semigroups
2012/4/16
Markov chain models had proved to be useful tools in many fields, such as physic, chemistry, information sciences, economics, finances, mathematical biology, social sciences, and statistics for analyz...
Boundary growth in one-dimensional cellular automata
Boundary growth one-dimensional cellular automata
2012/4/26
We systematically study the boundaries of one-dimensional, 2-color cellular automata depending on 4 cells, begun from simple initial conditions. We determine the exact growth rates of the boundaries t...
Coloring, location and domination of corona graphs
Coloring domination location Roman domination corona graphs
2012/4/18
A vertex coloring of a graph $G$ is an assignment of colors to the vertices of $G$ such that every two adjacent vertices of $G$ have different colors. A coloring related property of a graphs is also a...
Complete enumeration of small realizable oriented matroids
Complete enumeration small realizable oriented matroids Combinatorics
2012/4/18
Enumeration of all combinatorial types of point configurations and polytopes is a fundamental problem in combinatorial geometry. Although many studies have been done, most of them are for 2-dimensiona...
Domination related parameters in rooted product graphs
Domination location domination related parameters rooted product graphs
2012/4/18
A set $S$ of vertices of a graph $G$ is a dominating set in $G$ if every vertex outside of $S$ is adjacent to at least one vertex belonging to $S$. A domination parameter of $G$ is related to those se...
Matrix algorithm for determination of the elementary paths and elementary circuits using exotic semirings
idempotent semiring semiring of distinguished languages elementary path
2012/4/18
We propose a new method for determining the elementary paths and elementary circuits in a directed graph. Also, the Hamiltonian paths and Hamiltonian circuits are enumerated.
Combinatorial specification of permutation classes
permutation classes excluded patterns substitution decomposition simple permutations generating functions combinatorial specification random generation
2012/4/23
This article presents a methodology that automatically derives a combinatorial specification for the permutation class C = Av(B), given its basis B of excluded patterns and the set of simple permutati...
Generalized Measures of Edge Fault Tolerance in (n,k)-star Graphs
Combinatorics fault-tolerant analysis (n, k)-star graphs edge-connectivity h-super edge-connectivity
2012/4/18
This paper considers a kind of generalized measure $\lambda_s^{(h)}$ of fault tolerance in the $(n,k)$-star graph $S_{n,k}$ for $2\leqslant k \leqslant n-1$ and $0\leqslant h \leqslant n-k$, and deter...
Note on group distance magic graphs $G[C_4]$
distance magic labeling magic constant sigma labeling graph labeling Abelian group
2012/4/23
A \emph{group distance magic labeling} or a $\gr$-distance magic labeling of a graph $G(V,E)$ with $|V | = n$ is an injection $f$ from $V$ to an Abelian group $\gr$ of order $n$ such that the weight $...
Bondage number of grid graphs
Domination bondage number Cartesian product graph strong product graphs direct product graphs
2012/4/18
The bondage number $b(G)$ of a nonempty graph $G$ is the cardinality of a smallest set of edges whose removal from $G$ results in a graph with domination number greater than the domination number of $...
Henneberg constructions of some sparse colored graphs
Henneberg constructions some sparse colored graphs Combinatorics
2012/4/18
We give Henneberg-type constructions for some families of sparse colored graphs arising in rigidity theory periodic and forced symmetric frameworks. The proof method, which works with Laman-sparse fin...
On the strong metric dimension of corona product graphs and join graphs
Strong metric dimension strong resolving sets strong metric basis clique number corona graph
2012/4/18
Let $G$ be a connected graph. A vertex $w$ strongly resolves a pair $u$, $v$ of vertices of $G$ if there exists some shortest $u-w$ path containing $v$ or some shortest $v-w$ path containing $u$. A se...
Computing global offensive alliances in Cartesian product graphs
Global offensive alliances domination Cartesian product graphs
2012/4/18
A global offensive alliance in a graph $G$ is a set $S$ of vertices with the property that every vertex not belonging to $S$ has at least one more neighbor in $S$ than it has outside of $S$. The globa...
Interlacement in 4-regular graphs: a new approach using nonsymmetric matrices
4-regular graph circuit partition Euler system interlacement
2012/4/18
Let F be a 4-regular graph with an Euler system C. We introduce a simple way to modify the interlacement matrix of C so that every circuit partition P of F has an associated modified interlacement mat...