Decomposing Complete Graphs into a Graph Pair of Order 6

Firstly, a graph G consists of a vertex set V (G), and an edge set E (G) of endpoints which relate two vertices with each edge. Also, a decomposition of a graph is a list of subgraphs such that each edge appears in exactly one subgraph in the list. In the field of graph theory, graph decomposition is an active field of research. A graph pair is a pair of graphs on the same vertex set whose union is the complete graph. Abueida and Daven studied decompositions of complete graphs into graph-pairs of order four and five. We are extending their results by investigating which complete graphs decompose into a specific graph pair of order 6

Multidesigns for a Graph Pair of Order 6

Oral presentation abstract

c7 and C7 Complement Multidecomposition of Kn

Poster presentation abstract

A Look at Multi-Decompositions of Complete Graphs into Graph Pairs of Order 4

Firstly, a graph G consists of a vertex set V (G), and an edge set E (G) of endpoints which relate two vertices with each edge. Also, a decomposition of a graph is a list of subgraphs such that each edge appears in exactly one subgraph in the list. In the field ofgraph theory, graph decomposition is an active field of research. One type of decomposition is graph pairs. A graph pair is a pair of graphs on the same vertex set whose union is the complete graph. Abueida and Daven studieddecompositions of complete graphs into graph-pairs of order four. In their proof, they left a small part to the readers. We will complete this proof

Integer Antimagic Labeling for Cycle with One Chord

Poster presentation abstract

In Pursuit of the Ringel-Kotzig Conjecture: Uniform K-Distant Trees are Graceful

Graph labeling has been an active area of research since 1967, when Rosa introduced the concept. Arguably, the biggest open conjecture in the field is referred to as the Ringel-Kotzig conjecture, which states that all trees admit a graceful labeling. In this talk, we will give a bit of background on the problem, as well as present our own results. Namely, that a certain infinite class of trees (called uniform k-distant trees) admits a graceful labeling

Multidecomposition of Complete Directed Graphs Into Directed Graph Pairs of Order 3 and 4

Oral presentation abstract

Multidecompositions of Complete Graphs into a Graph Pair of Order 6

A graph is a mathematical structure consisting of a set of objects called vertices and a set of 2-element subsets of vertices, called edges. The complete graph on n vertices is the graph with n vertices and an edge between any pair of distinct vertices. Let C6 denote the cycle on 6 vertices. We are interested in partitioning the edges of the complete graph on n vertices into copies of C6 and its complement with at least one copy of each graph. We provide necessary and sufficient conditions on n for the existence such a structure