2025/08/14 by Choudhury, Projesh Nath, Nandi, Raju
#05C12 #05C50 #05C76 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2508.10834
The quadratic embedding constant (QEC) of a finite, simple, connected graph originated from the classical work of Schoenberg [Ann. of Math., 1935] and [Trans. Amer. Math. Soc., 1938] on Euclidean distance geometry. In this article, we study the QEC of graphs in terms of two graph operations: the Cartesian product and the join of graphs. We derive a general formula for the QEC of the join of an arbitrary graph with a regular graph and with a complete multipartite graph. We then provide quadratic embedding constants for the Cartesian product of an arbitrary graph G with a complete graph and with a complete bipartite graph in terms of QEC(G).