Sumset Valuations of Graphs and Their Applications

International audienc

Labeling Generating Matrices

This paper is mainly devoted to generate (special)(super) edge-magic labelings of graphs using matrices. Matrices are used in order to find lower bounds for the number of non-isomorphic (special)(super) edge-magic labelings of certain types of graphs. Also new applications of graph labelings are discussed

Decomposing 8-regular graphs into paths of length 4

A $T$-decomposition of a graph $G$ is a set of edge-disjoint copies of $T$ in $G$ that cover the edge set of $G$. Graham and H\"aggkvist (1989) conjectured that any $2\ell$-regular graph $G$ admits a $T$-decomposition if $T$ is a tree with $\ell$ edges. Kouider and Lonc (1999) conjectured that, in the special case where $T$ is the path with $\ell$ edges, $G$ admits a $T$-decomposition $\mathcal{D}$ where every vertex of $G$ is the end-vertex of exactly two paths of $\mathcal{D}$, and proved that this statement holds when $G$ has girth at least $(\ell+3)/2$. In this paper we verify Kouider and Lonc's Conjecture for paths of length $4$

On Properties of r\u3csub\u3ew\u3c/sub\u3e-Regular Graphs

If every vertex in a graph G has the same degree, then the graph is called a regular graph. That is, if deg(v) = r for all vertices in the graph, then it is denoted as an r-regular graph. A graph G is said to be vertex-weighted if all of the vertices are assigned weights. A generalized definition for degree regularity for vertex-weighted graphs can be stated as follows: A vertex-weighted graph is said to be rw-regular if the sum of the weights in the neighborhood of every vertex is rw. If all vertices are assigned the unit weight of 1, then this is equivalent to the definition for r-regular graphs. In this thesis, we determine if a graph has a weighting scheme that makes it a weighted regular graph or prove no such scheme exists for a number of special classes of graphs such as paths, stars, caterpillars, spiders and wheels

Finding Edge and Vertex Induced Cycles within Circulants.

Let H be a graph. G is a subgraph of H if V (G) ⊆ V (H) and E(G) ⊆ E(H). The subgraphs of H can be used to determine whether H is planar, a line graph, and to give information about the chromatic number. In a recent work by Beeler and Jamison [3], it was shown that it is difficult to obtain an automorphic decomposition of a triangle-free graph. As many of their examples involve circulant graphs, it is of particular interest to find triangle-free subgraphs within circulants. As a cycle with at least four vertices is a canonical example of a triangle-free subgraph, we concentrate our efforts on these. In this thesis, we will state necessary and sufficient conditions for the existence of edge induced and vertex induced cycles within circulants

Enumerating super edge-magic labelings for some types of path-like trees

The main goal of this paper is to use a variation of the Kronecker product of matrices in order to obtain lower bounds for the number of non isomorphic super edge-magic labelings of some types of path-like trees. As a corollary of the results obtained here we also obtain lower bounds for the number of harmonious labelings of the same type of trees.Postprint (published version