EXTENSION OF M-POLYNOMIAL AND DEGREE BASED TOPOLOGICAL INDICES FOR NANOTUBE
EXTENSION OF M-POLYNOMIAL AND DEGREE BASED TOPOLOGICAL INDICES FOR NANOTUBE
A. Rajpoot, L. Selvaganesh
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Abstract
The M-polynomial of a graph G(V(G),E(G)) is defined as M(G;u,v) = Ei≤j mijuivj, where mij denotes the number of edges xy ∈ E(G) such that {dx,dy} = {i, j}, where dx, dy denote degree of the vertex x and y in the graph G(V (G), E(G)). In this paper, we show how to compute the degree-based indices such as Forgotten index, Reduced Second Zagreb index, Sigma index, Hyper-Zagreb index and Albertson index using the M-polynomial. In addition, we present as an application how to quickly and effectively compute the degree-based topological indices using M-polynomial for two car- bon nanotube structures, namely HC5C7[p, q] and V C5C7[p, q].
Keywords
M-Polynomial, Carbon Nanotubes, Degree-based topological index, Graph Polynomials
GEODETIC DOMINATION INTEGRITY IN GRAPHS
GEODETIC DOMINATION INTEGRITY IN GRAPHS
G. Balaraman, S. S. Kumar, R. Sundareswaran
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Abstract
Let G be a simple graph. A subset S ⊆ V (G) is a said to be a geodetic set if every vertex u ∈/ S lies on a shortest path between two vertices from S. The minimum cardinality of such a set S is the geodetic number g(G) of G. A subset D ⊆ V (G) is a dominating set of G if every vertex u ∈/ D has at least one neighbor in D. The domination number γ(G) is the minimum cardinality of a dominating set of G. A subset is said to be a geodetic dominating set of G if it is both a geodetic and a dominating set. The geodetic domination number γg(G) is the minimum cardinality among all geodetic dominating sets in G. The geodetic domination integrity of a graph G is defined by DIg(G) = min{|S| + m(G − S) : S is a geodetic dominating set of G}, where m(G − S) denotes the order of the largest component in G−S. In this paper, we study the concepts of geodetic dominating integrity of some families of graphs and derive some bounds for the geodetic domination integrity. Also we obtain geodetic domination integrity of some cartesian product of graphs.
Keywords
Geodetic Sets, Geodetic Dominating Sets, Geodetic Domination Integrity Sets
NEURAL NETWORK MODELING OF CONVECTION HEAT TRANSFER COEFFICIENT FOR THE CASSON NANOFLUID
NEURAL NETWORK MODELING OF CONVECTION HEAT TRANSFER COEFFICIENT FOR THE CASSON NANOFLUID
M. Shanmugapriya, P. Sangeetha
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Abstract
This paper presents applications of Artificial Neural Network (ANN) to de- velop a mathematical model of magnetohydrodynamic (MHD) flow and heat transfer in a Casson nanofluid. The model equations are solved numerically by Runge-Kutta Fehlberg method with shooting technique. In the developing ANN model, the performance of the various configuration were compared with various types of errors such as Mean Square Error (MSE), Mean Absolute Error (MAE) and Sum Square Error (SSE). The best ANN configuration incorporated two hidden layers with twenty five neurons in each hid- den layer was able to construct convective heat transfer coefficients with MSE, MAE and SSE of 0.006346, 0.009813 and 1.015423%, respectively, and had R2 of 0.741516. A good co-relation has been obtained between the predicted results and the numerical values.
Keywords
Artificial neural network (ANN), convective heat transfer coefficient, magne- tohydrodynamic, Casson nanofluid
BOTH A GRAPH AND ITS COMPLEMENT ARE SELF-CENTERED WITH IDENTICAL RADIUS
BOTH A GRAPH AND ITS COMPLEMENT ARE SELF-CENTERED WITH IDENTICAL RADIUS
A. C. Malaravan, A. W. Baskar
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Abstract
We show that a graph and its complement are self-centered with identical radius r only when r = 2. Further, we provide a construction of such a graph for any given order at least eight.
Keywords
Eccentricity, Self-centered graph, Complement (of a graph)
RECIPROCAL VERSION OF PRODUCT DEGREE DISTANCE OF CACTUS GRAPHS
RECIPROCAL VERSION OF PRODUCT DEGREE DISTANCE OF CACTUS GRAPHS
K. Pattabiraman, M. A. Bhat
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Abstract
Thereciprocalversionofproductdegreedistanceisaproductdegreeweighted version of Harary index defined for a connected graph G as RDD∗(G) = E (dG(x).dG(y)) , {x,y}⊆V (G) where dG(x) is the degree of the vertex x and dG(x,y) is the distance from x to y in G. This article is attain the value of RDD∗ of different types of cactus such as triangular, square and hexagonal chain cactus graphs.
Keywords
Topological index, Degree, distance, cactus graph.
BOUNDS ON HYPER-STATUS CONNECTIVITY INDEX OF GRAPHS
BOUNDS ON HYPER-STATUS CONNECTIVITY INDEX OF GRAPHS
K. Pattabiraman, A. Santhakumar
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Abstract
In this paper, we obtain the bounds for the hyper-status connectivity indices of a connected graph and its complement in terms of other graph invariants. In addi- tion, the hyper-status connectivity indices of some composite graphs such as Cartesian product, join and composition of two connected graphs are obtained. We apply some of our results to compute the hyper-status connectivity indices of some important classes of graphs.
Keywords
Wiener index, status connectivity index, composite graph.
REVAN WEIGHTED PI INDEX ON SOME PRODUCT OF GRAPHS
REVAN WEIGHTED PI INDEX ON SOME PRODUCT OF GRAPHS
M. Priyadharshini, P. Kandan, E. Chandrasekaran, A. J. Kennedy
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Abstract
In chemical graph thoery, PI index is an additive topological index which has been used to measure the characteristics of chemical compounds. In this paper we introduce the weighted version of PI index of graph called the Revan Weighted PI index and we have obtained it for the hierarchical product of graphs, cartesian product, subdi- vision and join of two graphs. Also we have derived this index for some molecular graphs.
Keywords
Hierarchical Product, Cartesian Product, Subdivision, Join, PI index, Weighted PI index, Revan index.
VERTEX COLORING EDGE WEIGHTINGS OF SOME SQUARE GRAPHS
VERTEX COLORING EDGE WEIGHTINGS OF SOME SQUARE GRAPHS
N. Paramaguru
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Abstract
A k-edge-weighting w of a graph G is an assignment of integer weight, w(e) ∈ {1,2,...,k}, to each edge e. A k-edge-weighting w induces a vertex coloring cbydefiningc(u)= E w(e)foreveryu∈V(G),whereu∼edenotethatuisan u∼e end-vertex of e. A k-edge-weighting w of a graph G is a vertex coloring of G if the in- duced coloring c is proper, i.e., c(u) ̸= c(v) for any edge uv ∈ E(G). In this paper, vertex coloring edge weighting of square of Cartesian product of paths is considered.
Keywords
edge weighting, vertex coloring, Cartesian product