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Conjectures and open problems on face antimagic evaluations of graphs
(Journal of Indonesian Mathematical Society, 2005)
On the degrees of a strongly vertex-magic graph
(Discrete Mathematics, 2006)
Let G=(V ,E) be a finite graph, where |V |=n2 and |E|=e1.A vertex-magic total labeling is a bijection from V ∪E to the set of consecutive integers {1, 2, . . . , n + e} with the property that for every v ∈ V , (v) +w∈N(v) ...
(a,d)-Edge-Antimagic Total Labelings of Caterpillars
(Lecture Notes in Computer Science, 2005)
For 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 ...
Bounds on the number of isolates in sum graph labeling
(Discrete Mathematics, 2001)
A simple undirected graph H is called a sum graph if there is a labeling L of the vertices
of H into distinct positive integers such that any two vertices u and v of H are adjacent if and only if there is a vertex w with ...
On d-antimagic labelings of prisms
(Ars Combinatoria, 2004)
Vertex-antimagic total labelings of graphs
(Discussiones Mathematicae Graph Theory, 2003)
In this paper we introduce a new type of graph labeling for a graph G(V;E) called an (a; d)-vertex-antimagic total labeling. In this labeling we assign to the vertices and edges the consecutive integers from 1 to |V| + |E| ...
On two conjectures concerning vertex magic total labelings of generalized Petersen graphs
(Bulletins of ICA, 2001)
A vertex-magic total labeling of a graph with $v$ vertices and $e$ edges is defined as a one-to-one map taking the vertices and edges onto the integers $1,2,\dots ,v+e$ with the property that the sum of the label on a ...
Edge-magic total labelings of wheels, fans and friendship graphs
(Bulletins of ICA, 2002)
An edge-magic total labeling on a graph with v vertices and e
edges will be defined as a one-to-one map taking the vertices and
edges onto the integers 1, 2, · · · , v+e with the property that the sum
of the label on ...
Diregularity of digraphs of out-degree three and order two less than Moore bound
(Proceeding of 12th Australasian Workshop on Combinatorial Algorithms, 2001)
It is easy to show that any digraph with out-degree at most $d \ge 2$, diameter $k \ge 2$ and order $n=d+d^2+\dots + d^k - 1$, that is, two less than Moore bound must have
all vertices of out-degree $d$. In other words, ...