scholarly journals Pure Links Between Graph Invariants and Large Cycle Structures

10.5772/36250 ◽  
2012 ◽  
Author(s):  
Zh.G. Nikoghosyan
Keyword(s):  
Graph Invariants ◽  
Cycle Structures ◽  
Large Cycle

scholarly journals Graph Invariants and Large Cycles: A Survey

2011 ◽  
Vol 2011 ◽  
pp. 1-11 ◽  
Author(s):  
Zh. G. Nikoghosyan
Keyword(s):  
Analytical Tool ◽  
Graph Invariants ◽  
Initial Graph ◽  
Special Cases ◽  
Powerful Analytical Tool ◽  
New Ideas ◽  
Large Cycle

Graph invariants provide a powerful analytical tool for investigation of abstract substructures of graphs. This paper is devoted to large cycle substructures, namely, Hamilton, longest and dominating cycles and some generalized cycles including Hamilton and dominating cycles as special cases. In this paper, we have collected 36 pure algebraic relations between basic (initial) graph invariants ensuring the existence of a certain type of large cycles. These simplest kind of relations having no forerunners in the area actually form a source from which nearly all possible hamiltonian results (including well-known Ore's theorem, Posa's theorem, and many other generalizations) can be developed further by various additional new ideas, generalizations, extensions, restrictions, and structural limitations.

Study on the "Phase Hopping" AC-AC Frequency Conversion Method with Approximately Continuous Frequencies

2020 ◽  
Vol 13 (8) ◽  
pp. 1217-1226
Author(s):  
Zhengwang Xu ◽  
Guozhuang Jiang ◽  
Ke Kun ◽  
Yuchun Yi
Keyword(s):  
Output Voltage ◽  
Frequency Conversion ◽  
Frequency Control ◽  
Actual Application ◽  
Power Frequency ◽  
Voltage Frequency ◽  
The Law ◽  
Large Cycle ◽  
Selection Of ◽  
Conversion Technology

Background: The output voltage frequency for the previously proposed "phase hopping" AC-AC frequency conversion technology is determined by the law that the number of output voltage cycles is reduced by one relative to the power frequency in a large cycle containing six jumps. According to the law, only a limited number of output frequencies, such as 37.5 Hz, 42.86 Hz and 45 Hz are found. Due to the large spacing between the output frequencies, the "phase hopping" frequency conversion technology is difficult to put into practical use. Methods: In this paper, the law of the output frequency control is generalized so that the number of output cycles in a large cycle is reduced by n relative to the power frequency. The analysis shows that the appropriate selection of large cycles, including the number of power frequency cycles and the value of n, can find more frequencies to be used. Reducing the interval between the output frequencies within 1Hz. Results: The analysis results were verified in simulation by MATLAB, and the harmonics and the feasibility of the actual application were analyzed. Conclusion: Finally, an experimental platform was built and an experimental analysis was carried out. The experimental results show that the theoretical and simulation analyses are correct.

scholarly journals Topological Indices of Para-line Graphs of V-Phenylenic Nanostructures

2019 ◽  
Vol 17 (1) ◽  
pp. 260-266 ◽  
Author(s):  
Imran Nadeem ◽  
Hani Shaker ◽  
Muhammad Hussain ◽  
Asim Naseem
Keyword(s):  
Chemical Properties ◽  
Topological Indices ◽  
Structural Chemistry ◽  
Line Graphs ◽  
Physical And Chemical Properties ◽  
Graph Invariants ◽  
Molecular Graphs ◽  
Physical And Chemical ◽  
And Chemical Properties

Abstract The degree-based topological indices are numerical graph invariants which are used to correlate the physical and chemical properties of a molecule with its structure. Para-line graphs are used to represent the structures of molecules in another way and these representations are important in structural chemistry. In this article, we study certain well-known degree-based topological indices for the para-line graphs of V-Phenylenic 2D lattice, V-Phenylenic nanotube and nanotorus by using the symmetries of their molecular graphs.

Some properties of subgroup complementary addition Cayley graphs on abelian groups

2021 ◽  
Author(s):  
Naveen Palanivel ◽  
Chithra A. Velu
Keyword(s):  
Cayley Graph ◽  
Abelian Groups ◽  
Cayley Graphs ◽  
Graph Invariants

In this paper, we introduce subgroup complementary addition Cayley graph [Formula: see text] and compute its graph invariants. Also, we prove that [Formula: see text] if and only if [Formula: see text] for all [Formula: see text] where [Formula: see text].

A Note on the Kirchhoff and Additive Degree-Kirchhoff Indices of Graphs

2015 ◽  
Vol 70 (6) ◽  
pp. 459-463 ◽  
Author(s):  
Yujun Yang ◽  
Douglas J. Klein
Keyword(s):  
Upper Bound ◽  
Extremal Graphs ◽  
Graph Invariants ◽  
Kirchhoff Index ◽  
Resistance Distance

AbstractTwo resistance-distance-based graph invariants, namely, the Kirchhoff index and the additive degree-Kirchhoff index, are studied. A relation between them is established, with inequalities for the additive degree-Kirchhoff index arising via the Kirchhoff index along with minimum, maximum, and average degrees. Bounds for the Kirchhoff and additive degree-Kirchhoff indices are also determined, and extremal graphs are characterised. In addition, an upper bound for the additive degree-Kirchhoff index is established to improve a previously known result.

scholarly journals Structural Pluralism in Gerald Finzi’s Earth and Air and Rain

2020 ◽  
Vol 4 (1) ◽  
Author(s):  
Natalie Burton
Keyword(s):  
Twentieth Century ◽  
Song Cycle ◽  
Structural Pluralism ◽  
Cycle Structures

The genre of song cycle is complex and heterogeneous. As well as attracting significant contention in relation to matters of typology, the inherent aesthetic issues that arise from any intermedial union of words and music are compounded in the potential narrative consequences of the song cycle. Advocating melopoetic practices, my research seeks to examine the different cycle structures that emerge within the twentieth-century, English repertory. Gerald Finzi’s Earth and Air and Rain, composed in 1936, has a somewhat ambiguous genesis and complex history in performance and publication. This article explores the work’s potential to be characterized by structural pluralism; that is, the possibility that there may be more than one way of understanding and navigating the cycle’s structure. The genre of song cycle is complex and heterogeneous. As well as attracting significant contention in relation to matters of typology, the inherent aesthetic issues that arise from any intermedial union of words and music are compounded in the potential narrative consequences of the song cycle. Advocating melopoetic practices, my research seeks to examine the different cycle structures that emerge within the twentieth-century, English repertory. Gerald Finzi’s Earth and Air and Rain, composed in 1936, has a somewhat ambiguous genesis and complex history in performance and publication. This article explores the work’s potential to be characterized by structural pluralism; that is, the possibility that there may be more than one way of understanding and navigating the cycle’s structure.

scholarly journals On Mostar and Edge Mostar Indices of Graphs

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Ali Ghalavand ◽  
Ali Reza Ashrafi ◽  
Mardjan Hakimi-Nezhaad
Keyword(s):  
Upper Bound ◽  
Graph Invariants ◽  
Open Questions ◽  
Bicyclic Graphs ◽  
Extremal Values

Let G be a graph with edge set E G and e = u v ∈ E G . Define n u e , G and m u e , G to be the number of vertices of G closer to u than to v and the number of edges of G closer to u than to v , respectively. The numbers n v e , G and m v e , G can be defined in an analogous way. The Mostar and edge Mostar indices of G are new graph invariants defined as M o G = ∑ u v ∈ E G n u u v , G − n v u v , G and M o e G = ∑ u v ∈ E G m u u v , G − m v u v , G , respectively. In this paper, an upper bound for the Mostar and edge Mostar indices of a tree in terms of its diameter is given. Next, the trees with the smallest and the largest Mostar and edge Mostar indices are also given. Finally, a recent conjecture of Liu, Song, Xiao, and Tang (2020) on bicyclic graphs with a given order, for which extremal values of the edge Mostar index are attained, will be proved. In addition, some new open questions are presented.

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