OALib Journal
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May 21, 2020Open    AccessArticle

Schultz and Modified Schultz Polynomials of Vertex Identification Chain for Square and Complete Square Graphs

Mahmood M. Abdullah, Ahmed M. Ali
In this paper, we find the polynomials, indices and average distance for Schultz and modified Schultz of vertex identification chain for 4-cycle and 4- cycle complete.


Aug 27, 2019Open    AccessArticle

Schultz and Modified Schultz Polynomials of Some Cog-Special Graphs

Ahmed M. Ali, Haitham N. Mohammed
For a connected graph G, the Schultz and modified Schultz polynomials are defined as, respectively, where the summations are taken over all unordered pairs of distinct vertices in V(G), is the degree of vertex u, is the distance between u and v and V(G) is the vertex set of G. In this paper, we find Schultz and modified Schultz polynomials of the Cog-special graphs such as a complete graph,
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Jul 11, 2017Open    AccessArticle

Sharp Upper Bounds for Multiplicative Degree Distance of Graph Operations

R. Muruganandam, R. S. Manikandan, M. Aruvi
In this paper, multiplicative version of degree distance of a graph is defined and tight upper bounds of the graph operations have been found.


Dec 09, 2016Open    AccessArticle

The Four-Color Theorem of Map-Making Proved by Construction

John W. Oller Jr.
The objective of this paper is to prove by simple construction, generalized by induction, that the bounded areas on any map, such as found on the surface of a sheet of paper or a spherical globe, can be colored completely with just 4 distinct colors. Rather than following the tradition of examining each of tens of thousands of designs that can be produced on a planar surface, the approach here is to all the ways that any given pla
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Oct 17, 2016Open    AccessArticle

Soft Vibrational Force on Stock Market Networks

Mehmet Ali Balci, Qmer Akgüller
Stock market networks commonly involve uncertainty, and the theory of soft sets emerges as a powerful tool to handle it. In this study, we present a soft analogue of the differential of a vibrational potential function acting on a stock market network as vibrational force. For this purpose, we first study the vibrational potential function operating on each vertex by using the Laplacian of the neighborhood graph, then applied the
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Jun 27, 2016Open    AccessArticle

Log-Concavity of Centered Polygonal Figurate Number Sequences

Fekadu Tolessa Gedefa
This paper investigates the log-concavity of the centered m-gonal figurate number sequences. The author proves that for m≥3, the sequence {Cn(m)}
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