Energy of binary labeled graphs

Document Type : Research Paper

Authors

1 Manipal Institute of Technology Manipal University

2 Manipal Institute of Technology, Manipal University

Abstract

‎‎‎Let $G$ be a graph with vertex set $V(G)$ and edge set $X(G)$ and consider the set $A=\{0,1\}$‎. ‎A mapping $l:V(G)\longrightarrow A$ is called binary vertex labeling of $G$ and $l(v)$ is called the label of the vertex $v$ under $l$‎. ‎In this paper we introduce a new kind of graph energy for the binary labeled graph‎, ‎the labeled graph energy $E_{l}(G)$‎. ‎It depends on the underlying graph $G$ and on its binary labeling‎, ‎upper and lower bounds for $E_{l}(G)$ are established‎. ‎The labeled energies of a number of well known and much studied families of graphs are computed‎.

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References

R. Balakrishnan (2004). The energy of a graph. Linear Algebra Appl.. 387, 287-295
R. B. Bapat (2011). Graphs and matrices. Springer - Hindustan Book Agency, London.
R. B. Bapat and S. Pati (2004). Energy of a graph is never an odd integer. Bull. Kerala Math. Assoc.. 1, 129-132
C. Adiga, A. Bayad, I. Gutman and S. A. Srinivas (2012). The minimum covering energy of a graph. Kragujevac J. Sci.. 34, 39-56
C. Adiga and M. Smitha (2009). On maximum degree energy of a graph. Int. J. Contemp. Math. Sci.. 4, 385-396
F. Harary (1989). Graph Theory. Narosa Publishing House.
I. Gutman (1978). The energy of a graph. Ber. Math. Stat. Sekt. Forschungsz. Graz.. 103, 1-22
I. Gutman and B. Zhou (2006). Laplacian energy of a graph. Linear Algebra Appl.. 414, 29-37
I. Gutman (2001). The energy of a graph. old and new results, in: A. Betten, A. kohnert, R. Laue, A. Wassermann and (Eds.), Algebraic combinatorics and applications, Springer-Verlag, Berlin. , 196-211
G. Indulal, I. Gutman and A. Vijayakumar (2008). On distance energy of graphs. MATCH Commun. Math. Comput.Chem.. 60, 461-472
P. G. Bhat and D. Nayak C. (2012). Balanced Labeling and balance index set of one point union of two complete graphs. International Journal of Computer Applications. 52 (13), 1-5
B. J. McClelland (1971). Properties of the latent roots of a matrix, the estimation of electron energies. J. Chem. Phys.. 54, 640-643
S. Pirzada and I. Gutman (2008). Energy of a graph is never the square root of an odd integer. Appl. Anal. Discrete Math.. 2, 118-121
B. Zhou (2004). The energy of a graph. MATCH Commun. Math. Comput. Chem.. 51, 111-118
B. Zhou (2004). On the energy of a graph. Kragujevac J. Sci.. 26, 5-12
Transactions on Combinatorics

Volume 2, Issue 3 - Serial Number 3
September 2013
Pages 53-67

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