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Odd-order Cayley graphs with commutator subgroup of order pq are hamiltonian
Cayley graph hamiltonian cycle commutator subgroup
2012/5/9
We show that if G is a nontrivial, finite group of odd order, whose commutator subgroup [G,G] is cyclic of order p^m q^n, where p and q are prime, then every connected Cayley graph on G has a hamilton...
On incompactness for chromatic number of graphs
set theory graphs chromatic number compactness non-reflecting stationary sets
2012/5/9
We deal with incompactness. Assume the existence of non-reflecting stationary set of cofinality kappa . We prove that one can define a graph G whose chromatic number is > kappa, while the chromatic nu...
A connection between the bipartite complements of line graphs and the line graphs with two positive eigenvalues
line graphs graph spectra complements Courant-Weyl inequalities
2012/4/16
In 1974 Cvetkovi\'c and Simi\'c showed which graphs $G$ are the bipartite complements of line graphs. In 2002 Borovi\'canin showed which line graphs $L(H)$ have third largest eigenvalue $\lambda_3\leq...
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...
Connectivity Threshold of Random Geometric Graphs with Cantor Distributed Vertices
Cantor distribution connectivity threshold random geometric graph singular distributions
2012/4/18
For connectivity of \emph{random geometric graphs}, where there is no density for underlying distribution of the vertices, we consider $n$ i.i.d. \emph{Cantor} distributed points on $[0,1]$. We show 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...
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...
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 $...
Continuous-time distributed convex optimization on directed graphs
Continuous-time convex optimization directed graphs Optimization and Control
2012/4/17
This paper studies the continuous-time distributed optimization of a sum of convex functions over directed graphs. Contrary to what is known in the consensus literature, where the same dynamics works ...
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 $...
Bond percolation on isoradial graphs
Bond percolation isoradial graph rhombic tiling Penrose tiling inhomogeneous percolation universality
2012/4/18
In an investigation of percolation on isoradial graphs, we prove the criticality of canonical bond percolation on isoradial embeddings of planar graphs, thus extending celebrated earlier results for h...
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...