Recognizing generalized Sierpiński graphs

Generalized Graph Clustering: Recognizing (p, q)-Cluster Graphs

Cluster Editing is a classical graph theoretic approach to tackle the problem of data set clustering: it consists of modifying a similarity graph into a disjoint union of cliques, i.e, clusters. As pointed out in a number of recent papers, the cluster editing model is too rigid to capture common features of real data sets. Several generalizations have thereby been proposed. In this paper, we in...

Recognizing Generalized Transmission Graphs of Line Segments and Circular Sectors

Suppose we have an arrangement A of n geometric objects x1, . . . , xn ⊆ R in the plane, with a distinguished point pi in each object xi. The generalized transmission graph of A has vertex set {x1, . . . , xn} and a directed edge xixj if and only if pj ∈ xi. Generalized transmission graphs provide a generalized model of the connectivity in networks of directional antennas. The complexity class ...

Hamming dimension of a graph - The case of Sierpiński graphs

The Hamming dimension of a graph G is introduced as the largest dimension of a Hamming graph into which G embeds as an irredundant induced subgraph. An upper bound is proved for the Hamming dimension of Sierpiński graphs S k , k ≥ 3. The Hamming dimension of S 3 grows as 3. Several explicit embeddings are constructed along the way, in particular into products of generalized Sierpiński triangle ...

Sierpiński gasket graphs and some of their properties

Equitable L(2, 1)-labelings of Sierpiński graphs

An L(2, 1)-labeling of a graph G is equitable if the number of elements in any two color classes differ by at most one. The equitable L(2, 1)-labeling number λe(G) of G is the smallest integer k such that G has an equitable L(2, 1)-labeling. Sierpiński graphs S(n, k) generalize the Tower of Hanoi graphs—the graph S(n, 3) is isomorphic to the graph of the Tower of Hanoi with n disks. In this pap...