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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 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 ...
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, ...