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Journal of Mathematics
Volume 2016, Article ID 5906801, 11 pages
Research Article

On the Adjacency, Laplacian, and Signless Laplacian Spectrum of Coalescence of Complete Graphs

1Gogte Institute of Technology, Udyambag, Belagavi, Karnataka 59008, India
2Jain College of Engg, Machhe, Belagavi, Karnataka 590014, India

Received 23 June 2016; Accepted 3 August 2016

Academic Editor: Hong J. Lai

Copyright © 2016 S. R. Jog and Raju Kotambari. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Coalescence as one of the operations on a pair of graphs is significant due to its simple form of chromatic polynomial. The adjacency matrix, Laplacian matrix, and signless Laplacian matrix are common matrices usually considered for discussion under spectral graph theory. In this paper, we compute adjacency, Laplacian, and signless Laplacian energy ( energy) of coalescence of pair of complete graphs. Also, as an application, we obtain the adjacency energy of subdivision graph and line graph of coalescence from its energy.