• Title/Summary/Keyword: Well covered graphs

Search Result 2, Processing Time 0.019 seconds

ON CO-WELL COVERED GRAPHS

  • Abughazaleh, Baha';Abughneim, Omar;Al-Ezeh, Hasan
    • Communications of the Korean Mathematical Society
    • /
    • v.35 no.2
    • /
    • pp.359-370
    • /
    • 2020
  • A graph G is called a well covered graph if every maximal independent set in G is maximum, and co-well covered graph if its complement is a well covered graph. We study some properties of a co-well covered graph and we characterize when the join, the corona product, and cartesian product are co-well covered graphs. Also we characterize when powers of trees and cycles are co-well covered graphs. The line graph of a graph which is co-well covered is also studied.

THE INDEPENDENCE AND INDEPENDENT DOMINATING NUMBERS OF THE TOTAL GRAPH OF A FINITE COMMUTATIVE RING

  • Abughazaleh, Baha';Abughneim, Omar AbedRabbu
    • Communications of the Korean Mathematical Society
    • /
    • v.37 no.4
    • /
    • pp.969-975
    • /
    • 2022
  • Let R be a finite commutative ring with nonzero unity and let Z(R) be the zero divisors of R. The total graph of R is the graph whose vertices are the elements of R and two distinct vertices x, y ∈ R are adjacent if x + y ∈ Z(R). The total graph of a ring R is denoted by 𝜏(R). The independence number of the graph 𝜏(R) was found in [11]. In this paper, we again find the independence number of 𝜏(R) but in a different way. Also, we find the independent dominating number of 𝜏(R). Finally, we examine when the graph 𝜏(R) is well-covered.