Further studies on chromatic completion of graphs Toby B. Antony, Sudev Naduvath Discrete Mathematics Algorithms and Applications, 2026 The chromatic completion graph of [Formula: see text] with respect to a proper vertex coloring [Formula: see text] of [Formula: see text], denoted by [Formula: see text], is the graph obtained by adding all possible edges to [Formula: see text] without violating the proper coloring protocol. The maximum number of edges added to [Formula: see text] to obtain the chromatic completion graph is the chromatic completion number [Formula: see text]. Equitable chromatic completion graph [Formula: see text] of a graph [Formula: see text] and equitable chromatic completion number [Formula: see text] are the equitable analogues of [Formula: see text] and [Formula: see text], respectively. In this paper, we present various structural aspects of chromatic completion graphs and equitable chromatic completion graphs. Also, the chromatic completion and the related parameter are described in terms of adjacency matrix and color matrix of graphs. The equitable chromatic completion graph is shown to be a Turán graph. More relevantly, we obtained the equitable chromatic completion number of an arbitrary graph [Formula: see text].
Some improper injective coloring parameters of graphs Merlin Pious, S. Madhumitha, Sudev Naduvath Discrete Mathematics Algorithms and Applications, 2026 Any vertex coloring protocol of a graph can be viewed as a random experiment of assigning colors to the vertices, whose random variable is defined as the number of vertices assigned a specific color in that coloring. Based on this idea, the statistical parameters of mean and variance have been extended to chromatic mean and chromatic variance for various proper vertex colorings of graphs in the literature. In this paper, the ideas of chromatic mean and chromatic variance of graphs concerning their improper injective coloring are introduced and determined for certain standard graphs.
Certain variants of domatic partitions of n-inordinate invariant intersection graphs S. Madhumitha, Sudev Naduvath Asian European Journal of Mathematics, 2026 A class of algebraic intersection graphs, called the [Formula: see text]-inordinate invariant intersection graphs, are introduced in the literature and several properties of these graphs are being investigated. Domination in graphs is an important structural property and partitioning the vertex set of a graph into dominating sets is called the domatic partition of a graph. In this paper, we analyze the structure of the [Formula: see text]-inordinate invariant intersection graphs by investigating certain variants of domatic partitions of these graphs, that are defined based on different types of domination in graphs.
Some new results on anti-adjacency spectra of regular graphs D. Falguni Jain, Sudev Naduvath Asian European Journal of Mathematics, 2026 The anti-adjacency matrix [Formula: see text] of a simple graph [Formula: see text] with [Formula: see text], is a square matrix of order [Formula: see text] with rows and columns indexed by [Formula: see text], where the [Formula: see text]-entry [Formula: see text] is [Formula: see text], if the vertices [Formula: see text] and [Formula: see text] are not adjacent to each other and [Formula: see text], otherwise. The [Formula: see text]- entry of [Formula: see text] is [Formula: see text]. The anti-adjacency eigenvalues of [Formula: see text] are the eigenvalues obtained from the matrix [Formula: see text] and the corresponding spectra is called the anti-adjacency spectra of [Formula: see text], denoted by [Formula: see text]-spec([Formula: see text]). In this paper, we discuss the anti-adjacency spectra of join and disjoint union of regular graphs. The anti-adjacency spectra of bipartite regular graphs, line graphs of regular graphs and strongly regular graphs are also discussed.
A study on the invariant intersection graph of a graph S. Madhumitha, Sudev Naduvath Asian European Journal of Mathematics, 2026 Analyzing the structure of the automorphism groups of graphs, and investigating the properties of graphs that are constructed from algebraic structures are two important research topics in algebraic graph theory. Blending these two aspects of study, an algebraic intersection graph, called the invariant intersection graph of a graph, has been introduced in the literature. In this paper, we study certain properties of the invariant intersection graphs of graphs, and obtain some structural characterizations of these graphs, based on the automorphism group of the graph on which the invariant intersection graph is constructed.
The s-shunt non-intersection graph of a graph Vinny Susan Prebhath, Sudev Naduvath Discrete Mathematics Algorithms and Applications, 2026 For an integer [Formula: see text], an [Formula: see text] in a graph [Formula: see text] is a sequence of [Formula: see text] vertices [Formula: see text] of [Formula: see text] such that for all [Formula: see text], [Formula: see text], and for all [Formula: see text], [Formula: see text]. A non-intersection graph of the set of all [Formula: see text]-arcs on distinct vertices of [Formula: see text], that can be shunted onto some other [Formula: see text]-arc on distinct vertices of [Formula: see text], has been introduced. Basic properties based on the order, size and the degree of an arbitrary vertex of the non-intersection graph of a graph defined are obtained. Additionally, certain properties pertaining to the connectedness of the same are discussed.
On path-induced signed graphs J Kottarathil, S Naduvath Acta Universitatis Sapientiae, Mathematica 18 (1), 5 , 2026 2026 Citations: 3
Proper injective coloring parameters of some wheel-related graphs S Madhumitha, S Naduvath Journal of Interconnection Networks 26 (03), 2550009 , 2026 2026 Citations: 3
Equitable dominator coloring of helm-related graphs PS George, S Madhumitha, S Naduvath Journal of Interconnection Networks 26 (02), 2550004 , 2026 2026 Citations: 6
Some New Results on Equitable Dominator Coloring of Graphs PS George, S Naduvath Proyecciones (Antofagasta) 45 (2), 327-338 , 2026 2026
Chromatic Harmonic Polynomials and Indices of Jump Graphs of Some Graphs S Naduvath, J Kok, KP Chithra, A Ali International Journal of Foundations of Computer Science, 1-13 , 2026 2026
Some improper injective coloring parameters of graphs M Pious, S Madhumitha, S Naduvath Discrete Mathematics, Algorithms and Applications 18 (02), 2550026 , 2026 2026 Citations: 4
The -shunt non-intersection graph of a graph VS Prebhath, S Naduvath Discrete Mathematics, Algorithms and Applications, 2650029 , 2026 2026
Further studies on chromatic completion of graphs TB Antony, S Naduvath Discrete Mathematics, Algorithms and Applications 18 (02), 2550032 , 2026 2026
Some new results on anti-adjacency spectra of regular graphs DF Jain, S Naduvath Asian-European Journal of Mathematics 19 (02), 2540008 , 2026 2026
A Study on the Invariant Intersection Graph of a Graph S Madhumitha, S Naduvath Asian-European Journal of Mathematics , 2026 2026
The (Pk, I) Transformation Graph of VS Prebhath, S Naduvath Analysis, Algebra, and Associated Topics: ICEPAM 2024, Bathinda, India … , 2026 2026
Geodetic sets in -inordinate invariant intersection graphs S Madhumitha, S Naduvath Communications Faculty of Sciences University of Ankara Series A1 … , 2025 2025
Improper Injective Coloring Parameters of Certain Cycle-Related Graphs S Madhumitha, M Pious, S Naduvath Jordan Journal of Mathematics and Statistics 18 (4), 613-623 , 2025 2025
Cyclic property of iterative eccentrication of trees MR Raja, TA Mangam, J Kok, S Naduvath Asian-European Journal of Mathematics 18 (10), 2550043 , 2025 2025
On L (2, 1) Non-inverse Signed Graph of a Finite Group S Naduvath, D Bankapur Acta Universitatis Sapientiae, Informatica 17 (1), 7 , 2025 2025
-Shunt Intersection Graph of a Graph VS Prebhath, S Naduvath arXiv preprint arXiv:2507.16309 , 2025 2025 Citations: 2
Certain variants of domatic partitions of -inordinate invariant intersection graphs S Madhumitha, S Naduvath Asian-European Journal of Mathematics, 2540016 , 2025 2025
On -order sum signed graph of a finite group. D Bankapur, S Naduvath Discussiones Mathematicae: General Algebra & Applications 45 (2) , 2025 2025 Citations: 1
Rainbow Dominator Coloring of Some Cycle Related Graphs. S Madhumitha, S NADUVATH Creative Mathematics & Informatics 34 (3) , 2025 2025 Citations: 1
A study on upper deg-centric graphs TT Thalavayalil, J Kok, NK Sudev TWMS Journal of Applied and Engineering Mathematics , 2025 2025 Citations: 6
MOST CITED SCHOLAR PUBLICATIONS
On Weakly Uniform Integer Additive Set-Indexers of Graphs KA Germina, NK Sudev International Mathematical Forum 8 (37), 1827 - 1834 , 2013 2013 Citations: 84
On integer additive set-indexers of graphs NK Sudev, KA Germina International Journal of Mathematical Sciences and Engineering Applications … , 2014 2014 Citations: 71
Some new results on strong integer additive set-indexers of graphs NK Sudev, KA Germina Discrete Mathematics, Algorithms and Applications 7 (01), 1450065 , 2015 2015 Citations: 48
A Characterisation of weak integer additive Set-Indexers of graphs NK Sudev, KA Germina Journal of Fuzzy Set Valued Analysis 2014 (2014), 1-7 , 2014 2014 Citations: 38
On Chromatic Zagreb Indices of Certain Graphs J Kok, NK Sudev, U Mary Discrete mathematics, Algorithms and Applications 9 (2), 1-14 , 2017 2017 Citations: 32
Rainbow neighbourhood number of graphs J Kok, S Naduvath, MK Jamil Proyecciones Journal of Mathematics 38 (1), 8 Pages , 2019 2019 Citations: 26
On Certain J-Colouring Parameters of Graphs S Naduvath National Academy Science Letters , 2019 2019 Citations: 26
Weak integer additive set-indexers of certain graph operations NK Sudev, KA Germina Global Journal of Mathematical Sciences 8 , 2014 2014 Citations: 26
Certain Chromatic Sums of Some Cycle Related Graph Classes NK Sudev, KP Chithra, J Kok Discrete Mathematics, Algorithms and Applications 8 (3), 1-22 , 2016 2016 Citations: 25
A Note on the Sparing Number of Graphs NK Sudev, KA Germina Advances and Applications in Discrete Mathematics 14 (1), 51-65 , 2014 2014 Citations: 22
On certain parameters of equitable coloring of graphs NK Sudev, KP Chithra, S Satheesh, J Kok Discrete Mathematics, Algorithms and Applications 9 (04), 1750054 , 2017 2017 Citations: 21
On certain arithmetic integer additive set-indexers of graphs NK Sudev, KA Germina Discrete Mathematics, Algorithms and Applications 7 (03), 1550025 , 2015 2015 Citations: 21
A Study on Topological Integer Additive Set-Labeling of Graphs NK Sudev, KA Germina Electronic Journal of Graph Theory and Applications 3 (1), 70-84 , 2015 2015 Citations: 21
A study on integer additive set-graceful graphs NK Sudev, KA Germina Southeast Asian Bulletin of Mathematics 43 (5), 761-772 , 2019 2019 Citations: 19
Some Results on the -Colouring Parameters of Graphs NK Sudev, KP Chithra, J Kok Southeast Asian Bulletin of Mathematics 41 (6), 909-920 , 2017 2017 Citations: 17
On Arithmetic Integer Additive Set-Indexers of Graphs NK Sudev, KA Germina Journal of Advanced Research in Applied Mathematics 8 (8), 1-11 , 2016 2016 Citations: 17
Graphs on groups in terms of the order of elements: A review S Madhumitha, S Naduvath Discrete Mathematics, Algorithms and Applications 16 (03), 2330003 , 2024 2024 Citations: 16
On the curling number of certain graphs J Kok, N Sudev, C Sudev Southeast Asian Bulletin of Mathematics 42 (2), 195-209 , 2018 2018 Citations: 16
A study on the injective coloring parameters of certain graphs NK Sudev, KP Chithra, S Satheesh, J Kok Discrete Mathematics, Algorithms and Applications 8 (03), 1650052 , 2016 2016 Citations: 16
