3 citations · 3 across the 9 of their papers we have counts for
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Bounds on the Nodal Statuses of Some Transfinite Graphs
A. H. Zemanian
The bounds on the statuses of the nodes in a finite graph established by Entringer, Jackson, and Snyder are extended herein so that they apply to the nodes in a transfinite graph o…
The Galaxies of Nonstandard Enlargements of Transfinite Graphs of Higher Rsnks
A. H. Zemanian
In a prior work, the galaxies of the nonstandard enlargements of conventionally infinite graphs and also of transfinite graphs of the first rank of transfiniteness were defined, ex…
The Galaxies of Nonstandard Enlargements of Infinite and Transfinite Graphs
A. H. Zemanian
The galaxies of nonstandard enlargements of conventionally infinite as well as of transfinite graphs are defined, analyzed, and illustrated by some examples. It is then shown that…
Nonstandard Graphs, Revised
A. H. Zemanian
This is a revision of the paper archived previously on August 22, 2002. It corrects a mistake in Sec. 8 concerning eccentricities of graphs. From any given sequence of finite or in…
A Shorter Proof of the Transitivity of Transfinite Connectedness
A. H. Zemanian
A criterion is established for the transitivity of connectedness in a transfinite graph. Its proof is much shorter than a prior argument published previously for that criterion.
Ordinal Distances in Transfinite Graphs
A. H. Zemanian
An ordinal-valued metric taking its values in the set of all countable ordinals can be assigned to a metrizable set of nodes in a transfinite graph. Then, a variety of results conc…