116 research outputs found
Drawing a Graph in a Hypercube
A -dimensional hypercube drawing of a graph represents the vertices by
distinct points in , such that the line-segments representing the
edges do not cross. We study lower and upper bounds on the minimum number of
dimensions in hypercube drawing of a given graph. This parameter turns out to
be related to Sidon sets and antimagic injections.Comment: Submitte
Edge-antimagic graphs
AbstractFor a graph G=(V,E), a bijection g from V(G)∪E(G) into {1,2,…, |V(G)|+|E(G)|} is called (a,d)-edge-antimagic total labeling of G if the edge-weights w(xy)=g(x)+g(y)+g(xy), xy∈E(G), form an arithmetic progression starting from a and having common difference d. An (a,d)-edge-antimagic total labeling is called super (a,d)-edge-antimagic total if g(V(G))={1,2,…,|V(G)|}. We study super (a,d)-edge-antimagic properties of certain classes of graphs, including friendship graphs, wheels, fans, complete graphs and complete bipartite graphs
Inside-Out Polytopes
We present a common generalization of counting lattice points in rational
polytopes and the enumeration of proper graph colorings, nowhere-zero flows on
graphs, magic squares and graphs, antimagic squares and graphs, compositions of
an integer whose parts are partially distinct, and generalized latin squares.
Our method is to generalize Ehrhart's theory of lattice-point counting to a
convex polytope dissected by a hyperplane arrangement. We particularly develop
the applications to graph and signed-graph coloring, compositions of an
integer, and antimagic labellings.Comment: 24 pages, 3 figures; to appear in Adv. Mat
SUPER (a,d)-EDGE ANTIMAGIC TOTAL LABELING OF CONNECTED TRIBUN GRAPH
Abstract. A G graph of order p and size q is called an (a,d)-edge antimagic total if there exist a bijection f:V(G)∪E(G)⟶{1,2,…,p+q} such that the edge-weights, w(uv)=f(u)+f(v)+f(uv), uv∈E(G), form an arithmetic sequence with first term a and common difference d. Such a graph G is called super if the smallest possible labels appear on the vertices. In this paper we study super (a, d)-edge-antimagic total properties of connected Tribun graph. The result shows that a connected Tribun graph admit a super(a,d)-edge antimagic total labeling ford=0,1,2 for n≥1. It can be concluded that the result of this research has covered all the feasible n,d. Key Words: (a,d)-edge antimagic vertex labeling, super(a,d)-edge antimagic total labeling, Tribun Graph.
Antimagic Labelings of Weighted and Oriented Graphs
A graph is - if for any vertex weighting
and any list assignment with there exists an edge labeling
such that for all , labels of edges are pairwise
distinct, and the sum of the labels on edges incident to a vertex plus the
weight of that vertex is distinct from the sum at every other vertex. In this
paper we prove that every graph on vertices having no or
component is -weighted-list-antimagic.
An oriented graph is - if there exists an
injective edge labeling from into such that the
sum of the labels on edges incident to and oriented toward a vertex minus the
sum of the labels on edges incident to and oriented away from that vertex is
distinct from the difference of sums at every other vertex. We prove that every
graph on vertices with no component admits an orientation that is
-oriented-antimagic.Comment: 10 pages, 1 figur
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