Extended energy of some standard graphs
Downloads
DOI:
https://doi.org/10.26637/MJM0802/0032Abstract
This paper finds the extended energy of some special class of graphs and their complement graphs. Let $G=(V, E)$ be a simple graph with vertex set $V(G)=\left\{v_1, v_2, \ldots v_n\right\}$ and edge set $E(G)$. The Extended energy $E_{\text {ext }}(G)$ is defined to be the sum of the absolute eigen values of its extended adjacency matrix $A_{e x t}(G)$.
Keywords:
Extended adjacency matrix, spectral radius, spectrum of graphs, extended energyMathematics Subject Classification:
General Mathematics- Pages: 510-516
- Date Published: 01-04-2020
- Vol. 8 No. 02 (2020): Malaya Journal of Matematik (MJM)
I. Gutman, The energy of a graph, Ber. Math. Statist. Sekt. Forsch-ungszentram. Graz, 22(103)(1978), 1-22.
I. Gutman, Topology and stability of conjugated hydrocarbons: the dependence of total $pi$ - electron energy on molecular topology, J. Serb. Chem. Soc, 70(2005), $441-456$.
I. Gutman, X.Li, Y.Shi, Graph Energy, New York, Springer, 2012.
A.E. Brouwer, W.H. Haemers, Spectra of Graphs, Springer, 2010.
I. Gutman, The Energy of Graph-Old and New Results, Algebraic Combinatorics and Applications, Springer, Berlin, (2000), 196-211.
R.B. Bapat, S. Pati, Energy of a graph is never an odd integer, Bull. Kerala Math. Assoc., 1(2004), 129-132.
I. Gutman, B. Zhou, Laplacian energy of a graph, Linear Algebra and its Applications, 414(2006), 29-37.
T. Aleksic, Upper bounds for laplacian energy of graphs, Match Communications. Math. Comput. Chem., 60(2008), $435-439$.
R. Li, Some lower bounds for laplacian energy of graphs, Int. J. Contemp. Math. Sciences, 4(5)(2009), 219-223.
S. Pirzada, H.A.Ganie, On the laplacianeigen values of a graph and laplacian energy, Linear Algebra and its Applications, 486(2015), 454-468.
C. Adiga, E. Sampathkumar, M.A. Sriraj and A.S. Shrikanth, Color energy of graphs, Proc. JangjeonMath.Soc., 16(2013), 335-351.
P.G. Bhat, S.D'Souza, Color Laplacian energy of a graph, Proc. JangjeonMath.Soc., 18(2015), 321-330.
P.G. Bhat, S.D'Souza, ColorSignless Laplacian energy of a graphs, AKCE International Journal of Graphs and Combinatorics, (2017), 1-12.
Y. Yang, L. Xu, C.Y.Hu, Extended adjacency matrix indices and their applications, J. Chem. Inf. Comput. Sci, 34(1994), 1140-1145.
K. C. Das, I. Gutman, B. Furtula, On spectral radius and energy of extended adjacency matrix of graphs, Applied Mathematics and Computations, 296(2017), 116-123.
G. Indulal, I. Gutman, A. Vijayakumar, On distance energy of graphs, Match Communications. Math. Comput. Chem., 60(2008), 461-472
- NA
Similar Articles
- K.P. Vineesh, V. Anil Kumar, Neighbourhood \(V_4\)-magic labeling of some subdivision graphs , Malaya Journal of Matematik: Vol. 8 No. 04 (2020): Malaya Journal of Matematik (MJM)
- K.P. Vineesh, V. Anil Kumar, Neighbourhood \(V_4\)-magic labeling of some subdivision graphs , Malaya Journal of Matematik: Vol. 8 No. 02 (2020): Malaya Journal of Matematik (MJM)
You may also start an advanced similarity search for this article.
Metrics
Published
How to Cite
Issue
Section
License
Copyright (c) 2020 MJM
This work is licensed under a Creative Commons Attribution 4.0 International License.