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The rank of adjacency matrix plays an important role in construction of linear codes from a directed strongly regular graph using different techniques, namely, code orthogonality, adjacency matrix determinant and adjacency matrix spectrum. The problem of computing the dimensions of such codes is an intriguing one. Several conjectures to determine the rank of adjacency matrix of a DSRG Γ over a finite field, keep researchers working in this area. To address the same to an extent, we have considered the problem of finding the rank over a finite field of the adjacency matrix of a DSRG Γ (v , k , t , λ , μ) with μ = 1 , including some mixed Moore graphs and corresponding codes arising from them, in this paper. [ABSTRACT FROM AUTHOR]

This work generalizes the recently introduced bubble entropy (BE) algorithm for univariate time series to graph and network analysis. In this paper, we introduce a modified method, called bubble entropy for graph signals (BEG), as an invaluable tool for detecting the irregularity of signals defined on graphs. Our algorithm is based on using the adjacency matrix to combine the signal values with the topology of the graph. Experiments on both synthetic and real data demonstrate the availability of the proposed measures in detecting the irregularity of graph signals and identifying topological changes in graphs. [ABSTRACT FROM AUTHOR]

The comaximal graph Γ (R) of a commutative ring R is a simple graph with vertex set R and two distinct vertices u and v of Γ (R) are adjacent if and only if u R + v R = R. In this paper, we find the sharp bounds for the Sombor index for comaximal graphs of integer modulo ring ℤ n and give the corresponding extremal graphs. Also, we find the Sombor eigenvalues and the bounds for the Sombor energy of comaximal graphs of ℤ n . [ABSTRACT FROM AUTHOR]