On Topologies Induced by Graphs Under Some Unary and Binary Operations
2019 ◽
Vol 12
(2)
◽
pp. 499-505
Keyword(s):
Let G = (V (G),E(G)) be any simple undirected graph. The open hop neighborhood of v ϵ V(G) is the set 𝑁_𝐺^2(𝑣) = {u ϵ V(G): 𝑑_𝐺 (u,v) = 2}. Then G induces a topology τ_G on V (G) with base consisting of sets of the form F_G^2[A] = V(G) \ N_G^2 [A] where N_G^2 [A] = A ∪ {v ϵ V(G): 𝑁_𝐺^2(𝑣) ∩ A ≠ ∅ } and A ranges over all subsets of V (G). In this paper, we describe the topologies induced by the complement of a graph, the join, the corona, the composition and the Cartesian product of graphs.
1991 ◽
Vol 90
(3)
◽
pp. 297-311
◽
Keyword(s):
2007 ◽
Vol 28
◽
pp. 33-40
◽
2014 ◽
Vol 06
(01)
◽
pp. 1450001
◽
2016 ◽
Vol 36
(3)
◽
pp. 743
◽
2017 ◽
Vol 63
◽
pp. 287-294
◽
Keyword(s):
2017 ◽
Vol 340
(10)
◽
pp. 2398-2401
◽