TY - JOUR

T1 - The minimum vertex-vertex dominating Laplacian energy of a graph

AU - Sayinath Udupa, N. V.

AU - Bhat, R. S.

N1 - Funding Information:
We are indebted to the referees for their invaluable suggestions which has improved the overall presentation of the paper.
Publisher Copyright:
© 2022 World Scientific Publishing Company.

PY - 2022/7/1

Y1 - 2022/7/1

N2 - Let B(G) denote the set of all blocks of a graph G. Two vertices are said to vv-dominate each other if they are vertices of the same block. A set D ⊆ V is said to be vertex-vertex dominating set (vv-dominating set) if every vertex in G is vv-dominated by some vertex in D. The vv-domination number γvv = γvv(G) is the cardinality of the minimum vv-dominating set of G. In this paper, we introduce new kind of graph energy, the minimum vv-dominating Laplacian energy of a graph denoting it as LEvv(G). It depends both on the underlying graph of G and the particular minimum vv-dominating set of G. Upper and lower bounds for LEvv(G) are established and we also obtain the minimum vv-dominating Laplacian energy of some family of graphs.

AB - Let B(G) denote the set of all blocks of a graph G. Two vertices are said to vv-dominate each other if they are vertices of the same block. A set D ⊆ V is said to be vertex-vertex dominating set (vv-dominating set) if every vertex in G is vv-dominated by some vertex in D. The vv-domination number γvv = γvv(G) is the cardinality of the minimum vv-dominating set of G. In this paper, we introduce new kind of graph energy, the minimum vv-dominating Laplacian energy of a graph denoting it as LEvv(G). It depends both on the underlying graph of G and the particular minimum vv-dominating set of G. Upper and lower bounds for LEvv(G) are established and we also obtain the minimum vv-dominating Laplacian energy of some family of graphs.

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U2 - 10.1142/S1793557122501273

DO - 10.1142/S1793557122501273

M3 - Article

AN - SCOPUS:85117583156

SN - 1793-5571

VL - 15

JO - Asian-European Journal of Mathematics

JF - Asian-European Journal of Mathematics

IS - 7

M1 - 2250127

ER -