TY - JOUR
TI - Supercliques in a Graph
PY - 2022/07/31
Y2 - 2024/05/27
JF - European Journal of Pure and Applied Mathematics
JA - Eur. J. Pure Appl. Math.
VL - 15
IS - 3
DO - 10.29020/nybg.ejpam.v15i3.4480
UR - https://doi.org/10.29020/nybg.ejpam.v15i3.4480
SP - 1217-1228
AB - A set S ⊆ V (G) of a (simple) undirected graph G is a superclique in G if it is a clique and for every pair of distinct vertices v, w ∈ S, there exists u ∈ V (G) \ S such that u ∈ NG(v) \ NG(w) or u ∈ NG(w) \ NG(v). The maximum cardinality among the supercliques in G, denoted by ωs(G), is called the superclique number of G. In this paper, we determine the superclique numbers of some graphs including those resulting from some binary operations of graphs. We will also show that the difference of the clique number and the superclique number can be made arbitrarily large.
ER -