Vinayak V. Manjalapur

Karnatak University

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Harishchandra S. Ramane

Karnatak University

Madhura M. Mathai

Karnatak University

Gouramma A. Gudodagi

Karnatak University

Ajith S. Hanagawadimath

Karnatak University

Jia Liu

Peking University

Ashwini S. Yalnaik

Davangere University

V. B. Joshi

Karnatak University

Sharanu P. Sajjan

Shashank D. Shindhe

Karnatak University

Abdollah Alhevaz

University of Shahrood

Cooperative Institutions

Karnatak University

G.S. Science, Arts And Commerce College

Peking University

Hubei Academy of Agricultural Sciences

Southwest University of Science and Technology

Nanjing University of Chinese Medicine

Jinan University

Cellular Research (United States)

University of Toronto

Tianjin Medical University General Hospital

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On Extended Adjacency Index with Respect to Acyclic, Unicyclic and Bicyclic Graphs

Mathematics (2019)

Bin Yang Vinayak V. Manjalapur Sharanu P. Sajjan Madhura M. Mathai Jia Liu

For a (molecular) graph G, the extended adjacency index E A ( G ) is defined as Equation (1). In this paper we introduce some graph transformations which increase or decrease the extended adjacency ( E A ) index. Also, we obtain the extremal acyclic, unicyclic and bicyclic graphs with minimum and maximum of the E A index by a unified method, respectively.

Adjacency list

Topological index

Adjacency matrix

10.3390/math7070652

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Citations (3)

General sum-connectivity index, general product-connectivity index, general Zagreb index and coindices of line graph of subdivision graphs

AKCE International Journal of Graphs and Combinatorics (2017)

Harishchandra S. Ramane Vinayak V. Manjalapur Iván Gutman

The general sum-connectivity index, general product-connectivity index, general Zagreb index and coindices of line graphs of subdivision graphs of tadpole graphs, wheels and ladders have been reported in the literature. In this paper, we obtain general expressions for these topological indices for the line graph of the subdivision graphs, thus generalizing the existing results.

Topological index

10.1016/j.akcej.2017.01.002

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Citations (27)

Uniqueness of differential q-shift difference polynomials of entire functions

The Journal of Analysis (2021)

Madhura M. Mathai Vinayak V. Manjalapur

Transcendental function

Entire function

Transcendental equation

10.1007/s41478-020-00299-x

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Hamming index of graphs with respect to its incidence matrix

Indonesian Journal of Combinatorics (2022)

Harishchandra S. Ramane Ishwar B. Baidari Raju B. Jummannaver Vinayak V. Manjalapur Gouramma A. Gudodagi

Let $B(G)$ be the incidence matrix of a graph $G$. The row in $B(G)$ corresponding to a vertex $v$, denoted by $s(v)$ is the string which belongs to $\Bbb{Z}_2^n$, a set of $n$-tuples over a field of order two. The Hamming distance between the strings $s(u)$ and $s(v)$ is the number of positions in which $s(u)$ and $s(v)$ differ. In this paper we obtain the Hamming distance between the strings generated by the incidence matrix of a graph. The sum of Hamming distances between all pairs of strings, called Hamming index of a graph is obtained.

Hamming graph

Hamming distance

Incidence matrix

Hamming(7,4)

Hamming weight

Distance matrix

10.19184/ijc.2022.6.2.4

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On Complementary Distance Signless Laplacian Spectral Radius and Energy of Graphs

Iranian Journal of Mathematical Sciences and Informatics (2019)

Harishchandra S. Ramane Gouramma A. Gudodagi Vinayak V. Manjalapur Abdollah Alhevaz

Spectral Radius

Source

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Citations (1)

On Reciprocal Complementary Wiener Index of a Graph

Iranian journal of mathemathical chemistry./Iranian journal of mathemathical chemistry (2018)

Harishchandra S. Ramane V. B. Joshi Vinayak V. Manjalapur Shashank D. Shindhe

The eccentricity of a vertex v of graph G is the largest distance between and any other vertex of a graph . The reciprocal complementary Wiener (RCW) index of is defined as, , where D is the diameter of G and is the distance between the vertices and . In this paper we have obtained bounds for the index in terms of eccentricities and given an algorithm to compute the index.

Wiener index

Reciprocal

Topological index

Connectivity

Circulant graph

10.22052/ijmc.2017.69915.1259

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BOUNDS ON HARARY INDEX WITH RESPECT TO VERTEX CONNECTIVITY, INDEPENDENT NUMBER AND INDEPENDENT DOMINATION NUMBER OF A GRAPH

Advances in Mathematics Scientific Journal (2020)

Vinayak V. Manjalapur M.B. Rotti

Domination analysis

Topological index

10.37418/amsj.9.11.36

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