On \(\mathscr{P}\)-energy of join of graphs
Downloads
DOI:
https://doi.org/10.26637/MJM0804/0128Abstract
Given a graph \(G=(V, E)\) with a vertex partition \(\mathscr{P}\) of cardinality \(k\), we associate to it a real matrix \(A_{\mathscr{P}}(G)\), whose diagonal entries are the cardinalities of elements in \(\mathscr{P}\) and off-diagonal entries are from the set \(\{2,1,0,-1\}\). The \(\mathscr{P}\)-energy \(E_{\mathscr{P}}(G)\) is the sum of the absolute values of eigenvalues of \(A \mathscr{P}(G)\). In this paper, we discuss \(\mathscr{P}\)-energy of the join of graphs using the concept of \(M\)-coronal of graphs and determine \(\mathscr{P}\)-energy for the complements of the join of graphs.
Keywords:
Graph energy, partition energy, coronal of a graph, \(\mathscr{P}\)-energyMathematics Subject Classification:
Mathematics- Pages: 2082-2087
- Date Published: 01-10-2020
- Vol. 8 No. 04 (2020): Malaya Journal of Matematik (MJM)
C. Adiga, E. Sampathkumar, M. A. Sriraj and A. S Shrikanth, Color energy of a graph, Proc. Jangjeon Math Soc. 16(3) (2013), 335-351.
S. Y. Cui and G. X. Tian, The spectrum and the signless Laplacian spectrum of coronae, Linear Algebra Appl. 437(7) (2012), 1692-1703.
D. M. Cvetković , M. Doob and H. Sachs, Spectra of Graphs, Academic Press, New York, 1980.
I. Gutman, The energy of a graph, Ber. Math. Stat. SektForschungsz. Graz. 103 (1978), 1-22.
I. Gutman and B. Furtula, The total $pi$-electron energy saga, Croat. Chem. Acta. 90(3) (2017), 359-368, DOI 10.5562/cca3189
I. Gutman, X. Li, J. Zhang, Graph Energy, Springer, New York, 2012.
R. Hammack, W. Imrich, S. Klavžar, Handbook of product graphs, CRC press, 2011.
${ }^{[8]}$ P. B. Joshi and M. Joseph, $mathscr{P}$-energy of graphs, Acta Univ. Sapientiae, Info. 12(1) (2020), 137-157.
X. Liu, and Z. Zhang, Spectra of subdivision-vertex join and subdivision-edge join of two graphs, Bull. Malaysian Math. Sci. Soc. 42(1) (2019), 15-31.
C. McLeman and E. McNicholas, Spectra of coronae, Linear Algebra Appl., 435(5) (2011), 998-1007.
E. Sampathkumar and L. Pushpalatha, Complement of a graph: A generalization, Graphs Comb., 14(4) (1998), 377-392.
E. Sampathkumar, L. Pushpalatha, C. V. Venkatachalam and P. Bhat, Generalized complements of a graph, Indian J. Pure Appl. Math., 29(6) (1998), 625-639.
E. Sampathkumar, S. V. Roopa, K. A. Vidya, M. A. Sriraj, Partition energy of a graph, Proc. Jangjeon Math. Soc. 18(4) (2015), 473-493.
E. Sampathkumar and M. A. Sriraj, Vertex labeled/colored graphs, matrices and signed graphs, $J$. Comb. Inf. Syst. Sci. 38 (2013), 113-120.
D. B. West, Introduction to Graph Theory, Pearson, New Jersey, 2001.
F. Zhang (Ed.), The Schur Complement and its Applications, Springer Science & Business Media, 2006.
- NA
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.
