A subset $S$ of vertex set $V(D)$ is an {em indpendent dominating set} of $D$ if $S$ is both an independent and a dominating set of $D$. The {em indpendent domination number}, $i(D)$ is the cardinality of the smallest independent dominating set of $D$. In this paper we calculate the independent domination number of the { em cartesian product} of two {em directed paths} $P_m$ and $P_n$ for arbi...

the vertex arboricity $rho(g)$ of a graph $g$ is the minimum number of subsets into which the vertex set $v(g)$ can be partitioned so that each subset induces an acyclic graph‎. ‎a graph $g$ is called list vertex $k$-arborable if for any set $l(v)$ of cardinality at least $k$ at each vertex $v$ of $g$‎, ‎one can choose a color for each $v$ from its list $l(v)$ so that the subgraph induced by ev...

Let G be a group. The permutability graph of subgroups of G, denoted by Γ(G), is a graph having all the proper subgroups of G as its vertices, and two subgroups are adjacent in Γ(G) if and only if they permute. In this paper, we classify the finite groups whose permutability graphs are toroidal or projective-planar. In addition, we classify the finite groups whose permutability graph does not c...

We present a new algorithm to compute periodic (planar) straight-line drawings of toroidal graphs. Our algorithm is the rst to achieve two important aesthetic criteria: the drawing ts in a straight rectangular frame, and the grid area is polynomial, precisely the grid size is O(n×n). This solves one of the main open problems in a recent paper by Duncan et al. [3].

The Honeycomb toroidal graph is a highly symmetric, vertex-transitive, bipartite graph which has been investigated for certain properties including pan-cyclicity and Hamilton laceability. The main focus of this project was to construct generalised methods for finding Hamilton paths and thus provide a proof of Hamilton laceability for this graph. The resulting proof was successful for a subset o...

After summarizing the harmonic approach to topological coordinates and the null space embedding of graphs, three-coordinated tiling of the plane by hexagons, pentagons, and heptagons are presented and used for the construction of tubular, toroidal, and helical carbon structures. Physically realistic 3D geometries are formed from the corresponding adjacency matrices, and the final structure was ...

A graph G containing a perfect matching is said to be m-extendable if m ≤ (|V (G)| − 2)/2 and for every matching M with |M | = m, there is a perfect matching F in G such that M ⊆ F . In a previous paper, four of the present five authors characterized those quadrangulations of the torus which are 2-extendable. In the present work a characterization of those which are 3-extendable is obtained. Si...

The main focus of this work is to obtain upper bounds on the weighted chromatic number of some classes of graphs in terms of the weighted clique number. We first propose an 11 6 -approximation algorithm for multicoloring any weighted planar graph. We then study the multicoloring problem on powers of square and triangular meshes. Among other results, we show that the infinite triangular mesh is ...

Friday, October 28, 2016 1:00-1:10 Welcome by Suzanne Lenhart, NIMBioS Associate Director for Education & Outreach 1:10-2:00 Joaquin Bustoz, Jr. Lecture: Abdul-Aziz Yakubu, Howard University Mathematical Models for Malaria with Applications to Mali and USA Introduced by Suzanne Lenhart, NIMBioS 2:10-2:50 Federico Ardila, San Fransisco State University Using High-Dimensional Geometry to Move Rob...

We show the universality of the VEDIC network in simulating other well known interconnection networks b y generating the parameters of the VEDtC network automatically. Algorithms are given to represent chordal rings, toroidal meshes, binary hypercubes, kary n-cubes, and Cayley graphs star graph and pancake graph, as VEDIC networks. Using these parameters the VEDIC network can be used as a tool ...