14,591 research outputs found
Distance majorization sets in graphs
Let G = (V, E) be a simple graph. A subset D of V (G) is said to be a distance majorization set (or dm - set) if for every vertex u ∈ V − D, there exists a vertex v ∈ D such that d(u, v) ≥ deg(u) + deg(v). The minimum cardinality of a dm - set is called the distance majorization number of G (or dm - number of G) and is denoted by dm(G), Since the vertex set of G is a dm - set, the existence of a dm – set in any graph is guaranteed. In this paper, we find the dm - number of standard graphs like Kn, K1,n, Km,n, Cn, Pn, compute bounds on dm− number and dm- number of self complementary graphs and mycielskian of graphs.Publisher's Versio
The Lie h-Invariant Conformal Field Theories and the Lie h-Invariant Graphs
We use the Virasoro master equation to study the space of Lie h-invariant
conformal field theories, which includes the standard rational conformal field
theories as a small subspace. In a detailed example, we apply the general
theory to characterize and study the Lie h-invariant graphs, which classify the
Lie h-invariant conformal field theories of the diagonal ansatz on SO(n). The
Lie characterization of these graphs is another aspect of the recently observed
Lie group-theoretic structure of graph theory.Comment: 38p
On the editing distance of graphs
An edge-operation on a graph is defined to be either the deletion of an
existing edge or the addition of a nonexisting edge. Given a family of graphs
, the editing distance from to is the smallest
number of edge-operations needed to modify into a graph from .
In this paper, we fix a graph and consider , the set of
all graphs on vertices that have no induced copy of . We provide bounds
for the maximum over all -vertex graphs of the editing distance from
to , using an invariant we call the {\it binary chromatic
number} of the graph . We give asymptotically tight bounds for that distance
when is self-complementary and exact results for several small graphs
Perfect (super) Edge-Magic Crowns
A graph G is called edge-magic if there is a bijective function f from the set of vertices and edges to the set {1,2,…,|V(G)|+|E(G)|} such that the sum f(x)+f(xy)+f(y) for any xy in E(G) is constant. Such a function is called an edge-magic labelling of G and the constant is called the valence. An edge-magic labelling with the extra property that f(V(G))={1,2,…,|V(G)|} is called super edge-magic. A graph is called perfect (super) edge-magic if all theoretical (super) edge-magic valences are possible. In this paper we continue the study of the valences for (super) edge-magic labelings of crowns Cm¿K¯¯¯¯¯n and we prove that the crowns are perfect (super) edge-magic when m=pq where p and q are different odd primes. We also provide a lower bound for the number of different valences of Cm¿K¯¯¯¯¯n, in terms of the prime factors of m.Postprint (updated version
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