79 research outputs found
Super edge-magic deficiency of join-product graphs
A graph is called \textit{super edge-magic} if there exists a bijective
function from to such
that and is a
constant for every edge of . Furthermore, the \textit{super
edge-magic deficiency} of a graph is either the minimum nonnegative integer
such that is super edge-magic or if there exists no
such integer.
\emph{Join product} of two graphs is their graph union with additional edges
that connect all vertices of the first graph to each vertex of the second
graph. In this paper, we study the super edge-magic deficiencies of a wheel
minus an edge and join products of a path, a star, and a cycle, respectively,
with isolated vertices.Comment: 11 page
Regular graphs of odd degree are antimagic
An antimagic labeling of a graph with edges is a bijection from
to such that for all vertices and , the sum of
labels on edges incident to differs from that for edges incident to .
Hartsfield and Ringel conjectured that every connected graph other than the
single edge has an antimagic labeling. We prove this conjecture for
regular graphs of odd degree.Comment: 5 page
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
Enumerating super edge-magic labelings for the union of non-isomorphic graphs
A super edge-magic labeling of a graph G=(V,E) of order p and size q is a bijection f:V ∪E→{i}p+qi=1 such that: (1) f(u)+f(uv)+f(v)=k for all uv∈E; and (2) f(V )={i}pi=1. Furthermore, when G is a linear forest, the super edge-magic labeling of G is called strong if it has the extra property that if uv∈E(G) , u′,v′ ∈V (G) and dG (u,u′ )=dG (v,v′ )<+∞, then f(u)+f(v)=f(u′ )+f(v′ ). In this paper we introduce the concept of strong super edge-magic labeling of a graph G with respect to a linear forest F, and we study the super edge-magicness of an odd union of nonnecessarily isomorphic acyclic graphs. Furthermore, we find exponential lower bounds for the number of super edge-magic labelings of these unions. The case when G is not acyclic will be also considered.Preprin
Vertex-magic Labeling of Trees and Forests
A vertex-magic total labeling of a graph G(V,E) is a one-to-one map λ from E ∪ V onto the integers {1, 2, . . . , |E| + |V|} such that
λ(x) + Σ λ(xy) where the sum is over all vertices y adjacent to x, is a constant, independent of the choice of vertex x. In this paper we examine the existence of vertex-magic total labelings of trees and forests. The situation is quite different from the conjectured behavior of edge-magic total labelings of these graphs. We pay special attention to the case of so-called galaxies, forests in which every component tree is a star
On cordial labeling of hypertrees
Let be a vertex labeling of a hypergraph
. This labeling induces an~edge labeling of defined by
, where the sum is taken modulo . We say that is
-cordial if for all the number of vertices with
label differs by at most from the number of vertices with label and
the analogous condition holds also for labels of edges. If admits a
-cordial labeling then is called -cordial. The existence of
-cordial labelings has been investigated for graphs for decades.
Hovey~(1991) conjectured that every tree is -cordial for every .
Cichacz, G\"orlich and Tuza~(2013) were first to investigate the analogous
problem for hypertrees, that is, connected hypergraphs without cycles. The main
results of their work are that every -uniform hypertree is -cordial for
every and that every hypertree with or odd is -cordial.
Moreover, they conjectured that in fact all hypertrees are -cordial. In this
article, we confirm the conjecture of Cichacz et al. and make a step further by
proving that for every hypertree is -cordial.Comment: 12 page
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