## Randic type additive connectivity energy of a graph.(English)Zbl 1463.05346

Summary: The Randic type additive connectivity matrix of the graph $$G$$ of order $$n$$ and size $$m$$ is defined as $$RA(G)=(R_{ij})$$, where $$R_{ij}=\sqrt{d_i}+\sqrt{d_j}$$ if the vertices $$v_i$$ and $$v_j$$ are adjacent, and $$R_{ij}=0$$ if $$v_i$$ and $$v_j$$ are not adjacent, where $$d_i$$ and $$d_j$$ be the degrees of vertices $$v_i$$ and $$v_j$$ respectively. The purpose of this paper is to introduce and investigate the Randic type additive connectivity energy of a graph. In this paper, we obtain new inequalities involving the Randic type additive connectivity energy and presented upper and lower bounds for the Randic type additive connectivity energy of a graph. We also report results on Randic type additive connectivity energy of generalized complements of a graph.

### MSC:

 05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
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### References:

 [1] Gutman I., “The Energy of a Graph”, Ber. Math. Stat. Sekt. Forschungsz. Graz, 103 (1978), 1-22 [2] Gutman I., “The Energy of a Graph: Old and New Results”, Algebraic Combinatorics and its Applications, eds. Betten A., et al., Springer-Verlag, Berlin, 2001, 196-211 · Zbl 0974.05054 [3] Prakasha K. N., Siva Kota Reddy P., Cangül I. N., “Minimum Covering Randic Energy of a Graph”, Kyungpook Math. J., 57:4 (2017), 701-709 · Zbl 1397.05104 [4] Siva Kota Reddy P., Prakasha K. N., Siddalingaswamy V. M., “Minimum Dominating Randic Energy of a Graph”, Vladikavkaz. Math. J., 19:1, 28-35 · Zbl 1373.05111 [5] Sampathkumar E., Pushpalatha L., Venkatachalam C. V., Pradeep Bhat, “Generalized Complements of a Graph”, Indian J. Pure Appl. Math., 29:6 (1998), 625-639 · Zbl 0917.05066
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