The minimum vertex-block dominating energy of the graph

Sayinath Udupa, R. S. Bhat, Vinay Madhusudanan

Research output: Contribution to journalArticle

Abstract

Let B(G) denote the set of all blocks of a graph G. A vertex v G V and a block b G B(G) are said to block dominate (b-dominate) each other if v is in the block b. A set D C V is said to be a vertex block dominating set (VBD-set) if every block in G is b-dominated by some vertex in D. The vertex block domination number 7^5 = b(G) is the cardinality of the minimum vertex block dominating set of G. In this paper we introduce new kind of graph energy, the minimum vertex block dominating energy of the graph denoting it as Evb(G). It depends both on the underlying graph of G and the particular minimum vertex block dominating set (7^-set) of G. Upper and lower bounds for Evb(G) are established and we also obtain energy of some family of graphs.

Original languageEnglish
Pages (from-to)593-608
Number of pages16
JournalProceedings of the Jangjeon Mathematical Society
Volume22
Issue number4
DOIs
Publication statusPublished - 01-01-2019

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Graph in graph theory
Vertex of a graph
Energy
Dominating Set
Energy of Graph
Domination number
Upper and Lower Bounds
Cardinality
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All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Udupa, Sayinath ; Bhat, R. S. ; Madhusudanan, Vinay. / The minimum vertex-block dominating energy of the graph. In: Proceedings of the Jangjeon Mathematical Society. 2019 ; Vol. 22, No. 4. pp. 593-608.
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The minimum vertex-block dominating energy of the graph. / Udupa, Sayinath; Bhat, R. S.; Madhusudanan, Vinay.

In: Proceedings of the Jangjeon Mathematical Society, Vol. 22, No. 4, 01.01.2019, p. 593-608.

Research output: Contribution to journalArticle

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