Let G be a (p, q) graph. Let f : V (G) → {1, 2, . . . , k} be a map. For each edge uv, assign the label gcd (f(u), f(v)). f is called k-prime cordial labeling of G if |vf (i) − vf (j)| ≤ 1, i, j ∈ {1, 2, . . . , k} and |ef (0) − ef (1)| ≤ 1 where vf (x) denotes the number of vertices labeled with x, ef (1) and ef (0) respectively denote the number of edges labeled with 1 and not labeled with 1....

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...

In this paper we define extended corona and extended neighborhood corona of two graphs G1 and G2, which are denoted by G1 • G2 and G1 ∗ G2 respectively. We compute their adjacency spectrum, Laplacian spectrum and signless Laplacian spectrum. As applications, we give methods to construct infinite families of integral graphs, Laplacian integral graphs and expander graphs from known ones.

The set of eigenvalues of a graph together with their multiplicities is called the spectrum of . The knowledge of spectrum can be used to obtain various topological properties of graphs like connectedness, toughness and many more. In this paper we use MATLAB to completely describe the spectrum of Sierpiński graphs and Sierpiński triangles, thus adding to the classes of graphs whose spectrum is ...

For two graphs $mathrm{G}$ and $mathrm{H}$ with $n$ and $m$ vertices, the corona $mathrm{G}circmathrm{H}$ of $mathrm{G}$ and $mathrm{H}$ is the graph obtained by taking one copy of $mathrm{G}$ and $n$ copies of $mathrm{H}$ and then joining the $i^{th}$ vertex of $mathrm{G}$ to every vertex in the $i^{th}$ copy of $mathrm{H}$. The neighborhood corona $mathrm{G}starmathrm{H}$ of $mathrm{G}$ and $...