Maximum Euler Sombor Index of Unicyclic Graphs with Given Diameter , Sneha Sekar, Selvaraj Balachandran, , Suresh Elumalai, , Hechao Liu, and Match, 2026 The Euler Sombor (EU ) index of a graph G is defined aswhere dG(x) and dG(y) denote the degrees of vertex x and y in G, respectively.Biswaranjan Khanra, Shibsankar Das [Euler Sombor index of trees, unicyclic and chemical graphs, MATCH Commun.Math.Comput.Chem.94 (2025) 525-548], posed an open problem about determining the extremal values and extremal graphs for
Bounds on inverse sum indeg index of graph operations , Hanyuan Deng, Selvaraj Balachandran, , Suresh Elumalai, , S.G. Venkatesh, and Ars Combinatoria, 2025 <p>Let <span class="math inline">\\(G = (V(G), E(G))\\)</span> be a simple connected graph. The inverse sum indeg index of <span class="math inline">\\(G\\)</span>, denoted by <span class="math inline">\\(\\text{ISI}(G)\\)</span>, is defined as the sum of the weights <span class="math inline">\\(\\frac{d(u)d(v)}{d(u) + d(v)}\\)</span> of all edges <span class="math inline">\\(uv\\)</span> of <span class="math inline">\\(G\\)</span>, where <span class="math inline">\\(d(u)\\)</span> denotes the degree of a vertex in <span class="math inline">\\(G\\)</span>. In this paper, we first present some lower and upper bound for <span class="math inline">\\(ISI\\)</span> index in terms of graph parameters such as maximum degree, minimum degree and clique number. Moreover, we compute <span class="math inline">\\(ISI\\)</span> index of several graph operations like join, cartesian product, composition, corona and strong product of graphs.</p>
Maximum Atom-Bond Sum-Connectivity Index in Unicyclic Graphs of Fixed Girth , Palaniyappan Nithya, Suresh Elumalai, , Selvaraj Balachandran, , Hechao Liu, and Match, 2025 The ABS (atom-bond sum-connectivity) index of a graph G is given by the formula:where dx denotes the degree of vertex x in the graph G.The primary objective of this research paper is to identify the maximum, and second-maximum ABS index among all unicyclic graphs with a fixed girth.Additionally, we provide a characterization of the specific graphs that attain these extreme ABS values.
Maximum signless Laplacian Estrada index of tetracyclic graphs P. Nithya, Suresh Elumalai, Selvaraj Balachandran, Hechao Liu Filomat, 2025 In this study, we aim to determine the unique tetracyclic graph that maximizes the signless Laplacian Estrada index (SLEE) among all tetracyclic graphs. The SLEE of a graph ? is defined as the sum of the exponentials of its eigenvalues, expressed as follows: SLEE(?)=?n,i=1 esi, where s1, s2,...,sn are the eigenvalues of the signless Laplacian matrix of ?. By identifying this unique tetracyclic graph, we desire to understand the specific structural characteristics that contribute to the maximum SLEE within the class of tetracyclic graphs.
On the general zeroth-order randić index of bargraphs Discrete Mathematics Letters, 2019
A short note on Hyper Zagreb Index Suresh Elumalai, Toufik Mansour, Mohammad Ali Rostami, Gnanadhass Britto Antony Xavier Boletim Da Sociedade Paranaense De Matematica, 2019
Harary index of bipartite graphs Hanyuan Deng, , Selvaraj Balachandran, Suresh Elumalai, Toufik Mansour, , , and Electronic Journal of Graph Theory and Applications, 2019
Correcting the number of L-Borderenergetic Graphs of order 9 and 10 Match, 2018
Maximum and second maximum of geometric-arithmetic index of tricyclic graphs Match, 2018
