Article Per Year (5 Year)
p-Index From 2021 - 2026
0.23
P-Index
This Author published in this journals
All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
Richard M. Low
Department of Mathematics and Statistics, San Jose State University, San Jose, CA 95192, USA
Electrical & Electronics Engineering

Published : 2 Documents Claim Missing Document
Claim Missing Document
Check
Articles

Found 2 Documents
Search

 1 
Orthogonal embeddings of graphs in Euclidean space Wai Chee Shiu; Richard M. Low
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 7, No 2 (2019): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2019.7.2.13

Abstract

Let G = (V, E) be a simple connected graph. An injective function f : V → Rn is called an n-dimensional (or n-D) orthogonal labeling of G if uv, uw ∈ E implies that (f(v) − f(u)) ⋅ (f(w) − f(u)) = 0, where  ⋅  is the usual dot product in Euclidean space. If such an orthogonal labeling f of G exists, then G is said to be embedded in Rn orthogonally. Let the orthogonal rank or(G) of G be the minimum value of n, where G admits an n-D orthogonal labeling (otherwise, we define or(G) = ∞). In this paper, we establish some general results for orthogonal embeddings of graphs. We also determine the orthogonal ranks for cycles, complete bipartite graphs, one-point union of two graphs, Cartesian product of orthogonal graphs, bicyclic graphs without pendant, and tessellation graphs.
Computation of new diagonal graph Ramsey numbers Richard M. Low; Ardak Kapbasov; Arman Kapbasov; Sergey Bereg
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 10, No 2 (2022): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2022.10.2.17

Abstract

For various connected simple graphs G, we extend the table of diagonal graph Ramsey numbers R(G, G) in ‘An Atlas of Graphs.’ This is accomplished by first converting the calculation of R(G, G) into a satisfiability problem in propositional logic. Mathematical arguments and scientific computing are then used to calculate R(G, G).
Co-Authors Ardak Kapbasov Arman Kapbasov Sergey Bereg Wai Chee Shiu