3,648 research outputs found
The distance-regular graphs such that all of its second largest local eigenvalues are at most one
In this paper, we classify distance regular graphs such that all of its
second largest local eigenvalues are at most one. Also we discuss the
consequences for the smallest eigenvalue of a distance-regular graph. These
extend a result by the first author, who classified the distance-regular graph
with smallest eigenvalue .Comment: 16 pages, this is submitted to Linear Algebra and Application
Six signed Petersen graphs, and their automorphisms
Up to switching isomorphism there are six ways to put signs on the edges of
the Petersen graph. We prove this by computing switching invariants, especially
frustration indices and frustration numbers, switching automorphism groups,
chromatic numbers, and numbers of proper 1-colorations, thereby illustrating
some of the ideas and methods of signed graph theory. We also calculate
automorphism groups and clusterability indices, which are not invariant under
switching. In the process we develop new properties of signed graphs,
especially of their switching automorphism groups.Comment: 39 pp., 7 fi
Distance-regular graph with large a1 or c2
In this paper, we study distance-regular graphs that have a pair of
distinct vertices, say x and y, such that the number of common neighbors of x
and y is about half the valency of . We show that if the diameter is at
least three, then such a graph, besides a finite number of exceptions, is a
Taylor graph, bipartite with diameter three or a line graph.Comment: We submited this manuscript to JCT
A Heuristic Method of Generating Diameter 3 Graphs for Order/Degree Problem
We propose a heuristic method that generates a graph for order/degree
problem. Target graphs of our heuristics have large order (> 4000) and diameter
3. We describe the ob- servation of smaller graphs and basic structure of our
heuristics. We also explain an evaluation function of each edge for efficient
2-opt local search. Using them, we found the best solutions for several graphs.Comment: Proceedings of 10th IEEE/ACM International Symposium on
Networks-on-Chip, Nara, Japan, Aug. 201
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