BALANCED LAPLACIAN ENERGY OF A FRIENDSHIP GRAPH

B. Vijayalakshmi, K. Ameenal Bibi, R. Jothilakshmi

Abstract


Let G be a signed connected graph with order n and size m. The signed laplacian L ̅ is defined by L ̅ = D ̅- W, where D ̅ is signed degree matrix and W is a symmetric matrix with zero diagonal entries. The signed laplacian is a symmetric positive semidefinite. Let µ1 ≥ µ2 ≥ ....µn-1 ≥ µn = 0 be the eigen values of the laplacian matrix. The signed laplacian energy is defined as L ̅E(G) = ∑_(i=1)^n▒|μ_(i )-2m/n| . In this paper, we defined balanced signed laplacian energy of a Friendship graph. We also attained their upper bounds.

Subject Classification: 05C50, 05C69

Keywords


Balanced signed graph, Signed Laplacian matrix, Signed laplacian Energy of a Friendship graph.

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DOI: https://doi.org/10.26483/ijarcs.v8i6.4322

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