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Interrogation for Modernistic Conceptualization of Complementary Perfect Hop Domination Number with Various Grid Models

In: New Trends in Computational Vision and Bio-inspired Computing

Author

Listed:
  • G. Mahadevan

    (Gandhigram Rural Institute—Deemed to be University, Department of Mathematics)

  • V. Vijayalakshmi

    (Gandhigram Rural Institute—Deemed to be University, Department of Mathematics)

  • Selvam Aavadayappan

    (VHNSN College, Department of Mathematics)

Abstract

In this paper, we introduce the concept of Complementary perfect hop domination number of a graph. A set S ⊆ V is a hop dominating set of G, if every vertex v ∈ V − S there exists u ∈ S such that d(u,v) = 2. A set S ⊆ V is a complementary perfect hop dominating set of G if S is a hop dominating set and has atleast one perfect matching. The minimum cardinality of complementary perfect hop dominating set is called complementary perfect hop domination number of G and it is denoted by CPHD(G). Here, we investigate this CPHD number for some mirror graphs and some special type of graphs.

Suggested Citation

  • G. Mahadevan & V. Vijayalakshmi & Selvam Aavadayappan, 2020. "Interrogation for Modernistic Conceptualization of Complementary Perfect Hop Domination Number with Various Grid Models," Springer Books, in: S. Smys & Abdullah M. Iliyasu & Robert Bestak & Fuqian Shi (ed.), New Trends in Computational Vision and Bio-inspired Computing, pages 1219-1227, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-41862-5_123
    DOI: 10.1007/978-3-030-41862-5_123
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