Jongyook Park
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View article: An improved bound for strongly regular graphs with smallest eigenvalue $-m$
An improved bound for strongly regular graphs with smallest eigenvalue $-m$ Open
In 1979, Neumaier gave a bound on $λ$ in terms of $m$ and $μ$, where $-m$ is the smallest eigenvalue of a primitive strongly regular graph, unless the graph in question belongs to one of the two infinite families of strongly regular graphs…
View article: On non-bipartite graphs with integral signless Laplacian eigenvalues at most 6
On non-bipartite graphs with integral signless Laplacian eigenvalues at most 6 Open
In this paper, we completely classify the connected non-bipartite graphs with integral signless Laplacian eigenvalues at most 6.
View article: On directed strongly regular Cayley graphs over non-abelian groups with an abelian subgroup of index $2$
On directed strongly regular Cayley graphs over non-abelian groups with an abelian subgroup of index $2$ Open
In 1988, Duval introduced the concept of directed strongly regular graphs, which can be viewed as a directed graph version of strongly regular graphs. Such directed graphs have similar structural and algebraic properties to strongly regula…
View article: Improving the Delsarte bound
Improving the Delsarte bound Open
In this paper, we study the order of a maximal clique in an amply regular graph with a fixed smallest eigenvalue by considering a vertex that is adjacent to some (but not all) vertices of the maximal clique. As a consequence, we show that …
View article: On the nonexistence of pseudo-generalized quadrangles
On the nonexistence of pseudo-generalized quadrangles Open
In this paper we consider the question of when a strongly regular graph with parameters $((s+1)(st+1),s(t+1),s-1,t+1)$ can exist. These parameters arise when the graph is derived from a generalized quadrangle, but there are other examples …
View article: Partially metric association schemes with a multiplicity three
Partially metric association schemes with a multiplicity three Open
An association scheme is called partially metric if it has a connected relation whose distance-two relation is also a relation of the scheme. In this paper we determine the symmetric partially metric association schemes with a multiplicity…