Geodesic
Vertex-vertex color energy of a graph
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 2, pp. 1027-1034.

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In this paper we introduce new kind of graph energy, vv-color energy of a graph denoted as $E_{cvv}(G)$. It depends both on underlying graph $G$ and its coloring. Upper and lower bounds for $E_{cvv}(G)$ are established.
Keywords: energy of a graph, labeled graph, color energy of a graph, vv-coloring of a graph. 
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S. Udupa; R. S. Bhat. Vertex-vertex color energy of a graph. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 2, pp. 1027-1034. http://geodesic.mathdoc.fr/item/SEMR_2021_18_2_a38/

[1] C. Adiga, E. Sampathkumar, M.A. Siraj, A.S. Shrikanth, “Vertex labeled/colored graphs, matrices and signed graphs”, Proc. Jangjeon Math. Soc., 16 (2003), 335–351

[2] R.B. Bapat, Graphs and matrices, Hindustan Book Agency, New Delhi, 2011 | Zbl

[3] R.B. Bapat, S. Pati, “Energy of a graph is never be an odd integer”, Bull. Kerala Math. Assoc., 1 (2004), 129–132 | Zbl

[4] P.G. Bhat, R.S. Bhat, S.R. Bhat, “Relationship between block domination parameters of a graph”, Discrete Math. Algorithms Appl., 5:3 (2013), 1350018 | DOI | Zbl

[5] I. Gutman, “The energy of a graph”, Ber. Math.-Stat. Sekt. Forschungsz. Graz, 103 (1978), 1–22 | Zbl

[6] I. Gutman, X. Li, J. Zhang, “Graph energy”, Analysis of complex networks. From biology to linguistics, eds. M. Dehmer, F. Emmert-Streib, John Wiley Sons, Hoboken, 2009, 145–174 | DOI | Zbl

[7] I. Gutman, Bo Zhou, “Laplacian energy of a graph”, Lin. Algebra Appl., 414:1 (2006), 29–37 | DOI | Zbl

[8] F. Harary, Graph theory, Addison-Wesley, Reading, Mass. etc, 1969 | Zbl

[9] G. Indulal, I. Gutman, A. Vijaykumar, “On distance energy of graphs”, MATCH Commun. Math. Comput. Chem., 60:2 (2008), 461–472 | Zbl

[10] M.R. Jooyandeh, D. Kiani, M. Mirzakhah, “Incidence energy of a graph”, MATCH Commun. Math. Comput. Chem., 62:3 (2009), 561–572 | Zbl

[11] B.J. McClelland, “Properties of the latent roots of a matrix: The estimation of $\pi$-electron energies”, J. Chem. Phys., 54:2 (1971), 640–643 | DOI

[12] S. Udupa, R.S. Bhat, V. Madhusudanan, “The minimum vertex-block dominating energy of the graph”, Proc. Jangeon Math. Soc., 22:4 (2019), 593–608 | Zbl

[13] Sayinath Udupa, R.S. Bhat, “Strong vb-dominating and vb-independent sets of a graph”, Discrete Math. Algorithms Appl., 12:1 (2020), 2050002 | DOI | Zbl

[14] D.B. West, Introduction to graph theory, Prentice Hall, Upper Saddle River, 1996 | Zbl