Energy of Signed Spongy Hypercubes

Document Type: Research Paper


Yazd University


A spongy hypercube is a Cartesian product of a d-connected polyhedral graph and a k-dimensional hypercube‎. ‎The aim of this paper is to compute the energies of signed spongy hypercubes T□□(Q_k ) and O□□(Q_k )‎, ‎where T and O are tetrahedron and octahedron‎, ‎respectively‎.


Main Subjects

1. D. Cvetković, M. Doob and H. Sachs, Spectra of Graphs – Theory and Application, 3rd
edition, Johann Ambrosius Barth Verlag, Heidelberg–Leipzig, 1995.
2. K. A. Germina, K. S. Hameed and T. Zaslavsky, On product and line graphs of signed
graphs, their eigenvalues and energy, Linear Algebra Appl. 435 (2011) 2432–2450.
3. I. Gutman, The energy of a graph, Ber. Math.-Stat. Sekt. Forschungszent. Graz.103
(1978) 1−22.
4. I. Gutman, The energy of a graph: old and new results, Algebraic Combinatorics and
Applications (Gössweinstein, 1999), Springer, Berlin (2001)196−211.
5. I. Gutman and B. Furtula, Survey of graph energies, Math. Int. Res. 2 (2017) 85−129.
6. I. Gutman, General theory of cycle−dependence of total π−electron energy, Iranian J.
Math. Chem. 9 (2018) 1−9.
7. R. Hammack, W. Imrich and S. Klavžar, Handbook of Product Graphs, CRC Press,
London, 2016.
8. F. Harary, On the notion of balance of a signed graph, Michigan Math. J. 2 (1953)
9. A. Pîrvan−Moldovan and M. V. Diudea, Euler characteristic of polyhedral graphs,
Croat. Chem. Acta. 89 (2016) 471−479.
10. M. V. Diudea, Multi-Shell Polyhedral Clusters, Carbon Materials: Chemistry and
Physics, Springer International Publishing, Berlin, 2018.