Topological indices of the subdivision graph and the line graph of subdivision graph of the wheel graph

2021 ◽  
Vol 24 (2) ◽  
pp. 589-601
Author(s):  
Melaku Berhe Belay ◽  
Chunxiang Wang ◽  
Abdul Jalil M. Khalaf ◽  
Hamid Hosseini ◽  
Mohammad Reza Farahani
Keyword(s):  
Line Graph ◽  
Topological Indices ◽  
Subdivision Graph ◽  
Wheel Graph

VERTEX WEIGHTED WIENER POLYNOMIALS OF THE SUBDIVISION GRAPH AND THE LINE GRAPH OF SUBDIVISION GRAPH OF THE WHEEL GRAPH

2019 ◽  
Vol 20 (2) ◽  
pp. 305-320
Author(s):  
Zaheer Ahmad ◽  
Muhammad K. Jamil ◽  
Mohammad R. Farahani ◽  
Sudev Naduvath ◽  
Hafiz Muhammad Afzal Siddiqui
Keyword(s):  
Line Graph ◽  
Subdivision Graph ◽  
Wheel Graph

scholarly journals Distance Degree Index of Some Derived Graphs

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 283 ◽  
Author(s):  
Jianzhong Xu ◽  
Jia-Bao Liu ◽  
Ahsan Bilal ◽  
Uzma Ahmad ◽  
Hafiz Muhammad Afzal Siddiqui ◽  
...  
Keyword(s):  
Organic Molecules ◽  
Line Graph ◽  
Chemical Compounds ◽  
Topological Indices ◽  
Pharmacological Properties ◽  
Graph Structure ◽  
Total Graph ◽  
Graph Vertex ◽  
Physical Chemical ◽  
Subdivision Graph

Topological indices are numerical values associated with a graph (structure) that can predict many physical, chemical, and pharmacological properties of organic molecules and chemical compounds. The distance degree (DD) index was introduced by Dobrynin and Kochetova in 1994 for characterizing alkanes by an integer. In this paper, we have determined expressions for a DD index of some derived graphs in terms of the parameters of the parent graph. Specifically, we establish expressions for the DD index of a line graph, subdivision graph, vertex-semitotal graph, edge-semitotal graph, total graph, and paraline graph.

Topological Indices of the Line Graph of Subdivision Graph of Complete Bipartite Graphs

2017 ◽  
Vol 11 (6) ◽  
pp. 1631-1636 ◽  
Author(s):  
Adnan Aslam ◽  
Juan Luis Garc´ıa Guirao ◽  
Safyan Ahmad ◽  
Wei Gao
Keyword(s):  
Line Graph ◽  
Bipartite Graphs ◽  
Topological Indices ◽  
Subdivision Graph ◽  
Complete Bipartite Graphs

scholarly journals An Algebraic Approach to Find Some Topological Indices of Derived Graphs of the Benzene Ring

2021 ◽  
Vol 12 (4) ◽  
pp. 5431-5443
Keyword(s):  
Benzene Ring ◽  
Line Graph ◽  
Algebraic Approach ◽  
Chemical Compounds ◽  
Vital Role ◽  
Topological Indices ◽  
Zagreb Index ◽  
Subdivision Graph ◽  
Surface Network ◽  
P Type

Topological indices play a vital role in understanding the chemical and structural properties of the chemical compounds and nanostructures. By finding the M-polynomial of a graph representing a chemical compound, one can obtain the closed forms of some of the commonly known degree-based topological indices of the compound, such as the Zagreb index, general Randic ́ Index and harmonic index. In this article, we obtain the expression for the M-polynomial of the derived graphs of the Benzene ring embedded in the P-type surface network in 2D, namely the line graph, the subdivision graph, and the line graph of its subdivision. Furthermore, some of the degree-based topological indices are obtained for these graphs using their M-polynomials.

ON THE NORMALISED LAPLACIAN SPECTRUM, DEGREE-KIRCHHOFF INDEX AND SPANNING TREES OF GRAPHS

2015 ◽  
Vol 91 (3) ◽  
pp. 353-367 ◽  
Author(s):  
JING HUANG ◽  
SHUCHAO LI
Keyword(s):  
Lower Bound ◽  
Characteristic Polynomial ◽  
Regular Graph ◽  
Spanning Trees ◽  
Line Graph ◽  
Laplacian Spectrum ◽  
Kirchhoff Index ◽  
Subdivision Graph ◽  
Number Of Spanning Trees ◽  
Sharp Lower Bound

Given a connected regular graph $G$, let $l(G)$ be its line graph, $s(G)$ its subdivision graph, $r(G)$ the graph obtained from $G$ by adding a new vertex corresponding to each edge of $G$ and joining each new vertex to the end vertices of the corresponding edge and $q(G)$ the graph obtained from $G$ by inserting a new vertex into every edge of $G$ and new edges joining the pairs of new vertices which lie on adjacent edges of $G$. A formula for the normalised Laplacian characteristic polynomial of $l(G)$ (respectively $s(G),r(G)$ and $q(G)$) in terms of the normalised Laplacian characteristic polynomial of $G$ and the number of vertices and edges of $G$ is developed and used to give a sharp lower bound for the degree-Kirchhoff index and a formula for the number of spanning trees of $l(G)$ (respectively $s(G),r(G)$ and $q(G)$).

scholarly journals Computing topological indices of Hex Board and its line graph

2017 ◽  
Vol 1 (1) ◽  
pp. 62-71 ◽  
Author(s):  
Hafiz Mutee ur Rehman ◽  
◽  
Riffat Sardar ◽  
Ali Raza ◽  
◽  
...  
Keyword(s):  
Line Graph ◽  
Topological Indices

scholarly journals Topological properties of Graphene using some novel neighborhood degree-based topological indices

2019 ◽  
Vol 11 (01) ◽  
pp. 1950006 ◽  
Author(s):  
Sourav Mondal ◽  
Nilanjan De ◽  
Anita Pal
Keyword(s):  
Real Number ◽  
Chemical Structure ◽  
Topological Index ◽  
Line Graph ◽  
Topological Indices ◽  
Index Formula ◽  
Topological Properties ◽  
Zagreb Index ◽  
Physiochemical Properties ◽  
Second Zagreb Index

Topological indices are numeric quantities that transform chemical structure to real number. Topological indices are used in QSAR/QSPR studies to correlate the bioactivity and physiochemical properties of molecule. In this paper, some newly designed neighborhood degree-based topological indices named as neighborhood Zagreb index ([Formula: see text]), neighborhood version of Forgotten topological index ([Formula: see text]), modified neighborhood version of Forgotten topological index ([Formula: see text]), neighborhood version of second Zagreb index ([Formula: see text]) and neighborhood version of hyper Zagreb index ([Formula: see text]) are obtained for Graphene and line graph of Graphene using subdivision idea. In addition, these indices are compared graphically with respect to their response for Graphene and line graph of subdivision of Graphene.

scholarly journals Hyperbolicity on Graph Operators

Symmetry ◽  
2018 ◽  
Vol 10 (9) ◽  
pp. 360 ◽  
Author(s):  
J. Méndez-Bermúdez ◽  
Rosalío Reyes ◽  
José Rodríguez ◽  
José Sigarreta
Keyword(s):  
Line Graph ◽  
Discrete Mathematics ◽  
Total Graph ◽  
Subdivision Graph ◽  
Gromov Product

A graph operator is a mapping F : Γ → Γ ′ , where Γ and Γ ′ are families of graphs. The different kinds of graph operators are an important topic in Discrete Mathematics and its applications. The symmetry of this operations allows us to prove inequalities relating the hyperbolicity constants of a graph G and its graph operators: line graph, Λ ( G ) ; subdivision graph, S ( G ) ; total graph, T ( G ) ; and the operators R ( G ) and Q ( G ) . In particular, we get relationships such as δ ( G ) ≤ δ ( R ( G ) ) ≤ δ ( G ) + 1 / 2 , δ ( Λ ( G ) ) ≤ δ ( Q ( G ) ) ≤ δ ( Λ ( G ) ) + 1 / 2 , δ ( S ( G ) ) ≤ 2 δ ( R ( G ) ) ≤ δ ( S ( G ) ) + 1 and δ ( R ( G ) ) − 1 / 2 ≤ δ ( Λ ( G ) ) ≤ 5 δ ( R ( G ) ) + 5 / 2 for every graph which is not a tree. Moreover, we also derive some inequalities for the Gromov product and the Gromov product restricted to vertices.

scholarly journals Reformulated Zagreb Indices of Some Derived Graphs

Mathematics ◽  
2019 ◽  
Vol 7 (4) ◽  
pp. 366 ◽  
Author(s):  
Jia-Bao Liu ◽  
Bahadur Ali ◽  
Muhammad Aslam Malik ◽  
Hafiz Muhammad Afzal Siddiqui ◽  
Muhammad Imran
Keyword(s):  
Physical Properties ◽  
Chemical Structure ◽  
Topological Index ◽  
Chemical Reactivity ◽  
Line Graph ◽  
Total Graph ◽  
Zagreb Indices ◽  
Subdivision Graph ◽  
Chemical Constitution ◽  
Vertex Degrees

A topological index is a numeric quantity that is closely related to the chemical constitution to establish the correlation of its chemical structure with chemical reactivity or physical properties. Miličević reformulated the original Zagreb indices in 2004, replacing vertex degrees by edge degrees. In this paper, we established the expressions for the reformulated Zagreb indices of some derived graphs such as a complement, line graph, subdivision graph, edge-semitotal graph, vertex-semitotal graph, total graph, and paraline graph of a graph.

scholarly journals Line and Subdivision Graphs Determined by T4-Gain Graphs

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 926 ◽  
Author(s):  
Abdullah Alazemi ◽  
Milica Anđelić ◽  
Francesco Belardo ◽  
Maurizio Brunetti ◽  
Carlos M. da Fonseca
Keyword(s):  
Spectral Properties ◽  
Incidence Matrix ◽  
Multiplicative Group ◽  
Line Graph ◽  
Characteristic Polynomials ◽  
Signed Graphs ◽  
Subdivision Graph ◽  
Gain Graphs ◽  
The Relationship ◽  
Gain Graph

Let T 4 = { ± 1 , ± i } be the subgroup of fourth roots of unity inside T , the multiplicative group of complex units. For a T 4 -gain graph Φ = ( Γ , T 4 , φ ) , we introduce gain functions on its line graph L ( Γ ) and on its subdivision graph S ( Γ ) . The corresponding gain graphs L ( Φ ) and S ( Φ ) are defined up to switching equivalence and generalize the analogous constructions for signed graphs. We discuss some spectral properties of these graphs and in particular we establish the relationship between the Laplacian characteristic polynomial of a gain graph Φ , and the adjacency characteristic polynomials of L ( Φ ) and S ( Φ ) . A suitably defined incidence matrix for T 4 -gain graphs plays an important role in this context.

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