2 citations · 6 across the 15 of their papers we have counts for
17 papers
Characterizing the positive inertia index of connected signed graphs in terms of girth
Suliman Khan, Sakander Hayat, Mohammed J. F. Alenazi
Let be a connected signed graph and be its adjacency matrix. The positive inertia index of , denoted by , is defined as the number of positive…
Distance-regular graphs with a few -distance eigenvalues
Mamoon Abdullah, Brhane Gebremichel, Sakander Hayat +1
In this paper we study when the -distance matrix of a distance-regular graph has few distinct eigenvalues. We mainly concentrate on diameter 3.
Distance-regular graphs with exactly one positive -distance eigenvalue
Jack H. Koolen, Mamoon Abdullah, Brhane Gebremichel +1
In this paper, we study the -distance matrix for a distance-regular graph and show that the -distance matrix of a distance-regular graph with classical parameters ($D, q, α,…
Unique identification and domination of edges in a graph: The vertex-edge dominant edge metric dimension
H. M. Ikhlaq, S. Hayat, H. M. A. Siddiqui
Dominating sets and resolving sets have important applications in control theory and computer science. In this paper, we introduce an edge-analog of the classical dominant metric d…
On the Sombor index of graphs with given connectivity and number of bridges
Sakander Hayat, Muhammad Arshad, Kinkar Chandra Das
Recently in 2021, Gutman introduced the Sombor index of a graph, a novel degree-based topological index. It has been shown that the Sombor index efficiently models the thermodynami…
Extending a conjecture of Graham and Lovász on the distance characteristic polynomial
Aida Abiad, Boris Brimkov, Sakander Hayat +2
Graham and Lovász conjectured in 1978 that the sequence of normalized coefficients of the distance characteristic polynomial of a tree of order is unimodal with the maximum val…
On Sombor index of graphs with a given number of cut-vertices
Sakander Hayat, Ansar Rehman, Yubin Zhong
Introduced by Gutman in 2021, the Sombor index is a novel graph-theoretic topological descriptor possessing potential applications in the modeling of thermodynamic properties of co…
The Laplacian and normalized Laplacian spectra of Mobius polyomino networks and their applications
Zhi-Yu Shi, Jia-Bao Liu, Sakander Hayat
Spectral theory has widely used in complex networks and solved some practical problems. In this paper, we investigated the Laplacian and normalized Laplacian spectra of Mobius poly…
The normalized Laplacians and random walks of the parallel subdivision graphs
Jing Zhao, Jia-Bao Liu, Ying-Ying Tan +1
The -parallel subdivision graph is generated from which each edge of is replaced by parallel paths of length 2. The -parallel subdivision graph $S_{2k}(…
Resistance distance-based graph invariants and the number of spanning trees of linear crossed octagonal graphs
Jing Zhao, Jia-Bao Liu, Sakander Hayat
Resistance distance is a novel distance function, also a new intrinsic graph metric, which makes some extensions of ordinary distance. Let On be a linear crossed octagonal graph. R…
A spectral characterization of the s-clique extension of the square grid graphs
Sakander Hayat, Jack H. Koolen, Muhammad Riaz
In this paper we show that for integers , , any co-edge-regular graph which is cospectral with the -clique extension of the -grid is the -clique ex…
The multiplicative Zagreb indices of graphs with given connectivity or number of pendant vertices
Shengjin Ji, Shaohui Wang, Tilahun Muche +1
For a graph , the first multiplicative Zagreb index is the product of squares of vertex degrees, and the second multiplicative Zagreb index is the pr…
Graphs with two main and two plain eigenvalues
Sakander Hayat, Muhammad Javaid, Jack H. Koolen
In this paper, we introduce the concepts of the plain eigenvalue, the main-plain index and the refined spectrum of graphs. We focus on the graphs with two main and two plain eigenv…
A note on graphs with exactly two main eigenvalues
Sakander Hayat, Jack H. Koolen, Fenjin Liu +1
In this note, we consider connected graphs with exactly two main eigenvalues. We will give several constructions for them, and as a consequence we show a family of those graphs wit…
Bicyclic graphs with extremal degree resistance distance
Jia-Bao Liu, Si-Qi Zhangb, Xiang-Feng Pan +2
Let be the resistance distance between two vertices of a simple graph , which is the effective resistance between the vertices in the corresponding electrical ne…
Further results on degree based topological indices of certain chemical networks
Shaohui Wang, Jia-Bao Liu, Chunxiang Wang +1
There are various topological indices such as degree based topological indices, distance based topological indices and counting related topological indices etc. These topological i…
Hypercubes are determined by their distance spectra
Jack. H. Koolen, Sakander Hayat, Quaid Iqbal
We show that the d-cube is determined by the spectrum of its distance matrix.