Abstract Associative spectra of graph algebras are examined with the help homomorphisms DFS trees. Undirected graphs classified according to associative their algebras; there only three distinct possibilities: constant 1, powers 2, and Catalan numbers. antiassociative digraphs described, determined for certain families digraphs, such as paths, cycles, on two vertices.

given a graph $g$, let $g^sigma$ be an oriented graph of $g$ with the orientation $sigma$ and skew-adjacency matrix $s(g^sigma)$. then the spectrum of $s(g^sigma)$ consisting of all the eigenvalues of $s(g^sigma)$ is called the skew-spectrum of $g^sigma$, denoted by $sp(g^sigma)$. the skew energy of the oriented graph $g^sigma$, denoted by $mathcal{e}_s(g^sigma)$, is defined as the sum of the n...

Relative centricity RC values of vertices/atoms are calculated within the Distance Detour and Cluj-Distance criteria on their corresponding Shell transforms. The vertex RC distribution in a molecular graph gives atom equivalence classes, useful in interpretation of NMR spectra. Timed by vertex valences, RC provides a new index, called Centric Connectivity CC, which can be useful in the topologi...

let $g$ be a finite group and let $gk(g)$ be the prime graph of $g$. we assume that $ngeqslant 5 $ is an odd number. in this paper, we show that the simple groups $b_n(3)$ and $c_n(3)$ are 2-recognizable by their prime graphs. as consequences of the result, the characterizability of the groups $b_n(3)$ and $c_n(3)$ by their spectra and by the set of orders of maximal abelian subgroups are obtai...

In this paper, we define duplication corona, duplication neighborhood corona and duplication edge corona of two graphs. We compute their adjacency spectrum, Laplacian spectrum and signless Laplacian. As an application, our results enable us to construct infinitely many pairs of cospectral graphs and also integral graphs.