On the average degree eigenvalues and average degree energy of graphs

S. C. Patekar, S. A. Barde, M. M. Shikare

Abstract


Given a graph $G$ with $n$ vertices $v_1, v_2, \dots, v_n$ and the vertex degrees $d_1, d_2,...,d_n$ respectively. We associate to $G$ an average degree matrix $A_v(G)$ whose $(i,j)^{th}$ entry is $\frac{d_i + d_j}{2}$. We explore some properties of the eigenvalues and energy of $A_v(G)$.

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How to Cite this Article:

S. C. Patekar, S. A. Barde, M. M. Shikare, On the average degree eigenvalues and average degree energy of graphs, Journal of Mathematical and Computational Science, Vol 9, No 1 (2019), 46-59

Copyright © 2019 S. C. Patekar, S. A. Barde, M. M. Shikare. 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.

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