Energy and NEPS of graphs. (English) Zbl 1061.05060
The paper is aimed at studying noncomplete extended \(p\)-sums (NEPS) of simple graphs, each with at least two vertices. It consists of four sections, the first one containing definitions, symbols and theorems used in the other sections. The second section includes the proof of the theorem, reflecting equality of the energy of a product of graphs and the product of the energy of graphs, and examples illustrating constructions based on this theorem. The theorem in the third section proves that the energy of NEPS is not representable as a function of the energy of its factors, except for the product of graphs. Also proved is the theorem, bounding the energy of NEPS by a function of the energy and the number of vertices of its factors.
Reviewer: Vitali Oscarovich Groppen (Vladikavkaz)
MSC:
| 05C50 | Graphs and linear algebra (matrices, eigenvalues, etc.) |
| 05C75 | Structural characterization of families of graphs |
References:
| [1] | Balakrishnan R, Linear Algebra and its Applications |
| [2] | Brankov V, J. Serb. Chem. Soc. |
| [3] | Cvetković D, Spectra of Graphs – Theory and Application (1995) |
| [4] | Cvetković D, Univ. Beograd Publ. Elektrotehn. Fak., Ser. Mat. Fiz. 302 pp 67– (1970) |
| [5] | Gutman I, Ber. Math.–Statist. Sekt. Forschungszentrum Graz 103 pp 1– (1978) |
| [6] | Gutman I, Algebraic Combinatorics and Applications pp pp. 196–211– (2001) |
| [7] | Gutman I, Introduction to Chemical Graph Theory (in Serbian). (2003) |
| [8] | Gutman I, MATCH. Communications in Mathematical and in Computer Chemistry 43 pp 17– (2001) |
| [9] | Gutman I, Bull. Acad. Serbe Sci. Arts (Cl. Math. Natur.) 118 pp 35– (1999) |
| [10] | DOI: 10.1023/A:1010935321906 · Zbl 0977.05085 · doi:10.1023/A:1010935321906 |
| [11] | DOI: 10.1080/03081080108818705 · Zbl 0996.05092 · doi:10.1080/03081080108818705 |
| [12] | Hou Y, MATCH. Communications in Mathematical and in Computer Chemistry 43 pp 29– (2001) |
| [13] | DOI: 10.1016/S0024-3795(01)00609-7 · Zbl 1015.05052 · doi:10.1016/S0024-3795(01)00609-7 |
| [14] | DOI: 10.1006/aama.2000.0705 · Zbl 0976.05040 · doi:10.1006/aama.2000.0705 |
| [15] | DOI: 10.1007/s00373-002-0487-7 · Zbl 1015.05043 · doi:10.1007/s00373-002-0487-7 |
| [16] | Li J, Acta Applicandae Mathematicae. An International Survey Journal on Applying Mathematics and Mathematical Applications 14 pp 443– (1998) |
| [17] | DOI: 10.1016/S0024-3795(03)00540-8 · Zbl 1023.05094 · doi:10.1016/S0024-3795(03)00540-8 |
| [18] | Ramane H, Kragujevac Journal of Mathematics 26 (2004) |
| [19] | Stevanović D, Linear Algebra and its Applications 301 pp 137– (1999) · Zbl 0942.05034 · doi:10.1016/S0024-3795(99)00194-9 |
| [20] | Zhou B, MATCH. Communications in Mathematical and in Computer Chemistry 51 pp 111– (2004) |
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