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The power graph of a group is the graph whose vertex set is the group, two elements being adjacent if one is a power of the other. We observe that non-isomorphic finite groups may have isomorphic power graphs, but that finite abelian groups with isomorphic power graphs must be isomorphic. We conjecture that two finite groups with isomorphic power graphs… (More)

Interval graphs were used in the study of genomics by the famous molecular biologist Benzer. Later on probe interval graphs were introduced by Zhang as a generalization of interval graphs for the study of cosmid contig mapping of DNA. A tagged probe interval graph (briefly, TPIG) is motivated by similar applications to genomics, where the set of vertices is… (More)

A (simple undirected) graph G = (V, E) with m edges is graceful if it has a distinct vertex labeling f : V −→ {0, 1, 2, 3,. .. , m} which induces a set of distinct edge labels {|f (u) − f (v)| | uv ∈ E, u, v ∈ V }. The famous Ringel-Kotzig conjecture [9, 15] is that all trees are graceful. The base of a tree T is obtained from T by deleting its one-degree… (More)

This note explores the relation between the boxicity of undirected graphs and the Ferrers dimension of digraphs.