An oriented graph Gσ is a simple undirected graph G with an orientation, which assigns to each edge a direction so that Gσ becomes a directed graph. G is called the underlying graph of Gσ and we denote by S(Gσ) the skew-adjacency matrix of Gσ and its spectrum Sp(Gσ) is called the skew-spectrum of Gσ. In this paper, the coefficients of the characteristic polynomial of the skew-adjacency matrix S...

a connected graph g is said to be neighbourly irregular graph if no two adjacent vertices of g have same degree. in this paper we obtain neighbourly irregular derived graphs such as semitotal-point graph, k^{tℎ} semitotal-point graph, semitotal-line graph, paraline graph, quasi-total graph and quasivertex-total graph and also neighbourly irregular of some graph products.

Godsil-McKay switching is an operation on graphs that doesn’t change the spectrum of the adjacency matrix. Usually (but not always) the obtained graph is non-isomorphic with the original graph. We present a straightforward sufficient condition for being isomorphic after switching, and give examples which show that this condition is not necessary. For some graph products we obtain sufficient con...

A graph is said to be determined by the adjacency spectrum (DS for short) if there is no other nonisomorphic graph with the same spectrum. All connected graphs with index at most √ 2 + √ 5 are known. In this paper, we show that with few exceptions all of these graphs are DS. AMS Subject Classification: 05C50.

the order graph of a group $g$, denoted by $gamma^*(g)$, is a graph whose vertices are subgroups of $g$ and two distinct vertices $h$ and $k$ are adjacent if and only if $|h|big{|}|k|$ or $|k|big{|}|h|$. in this paper, we study the connectivity and diameter of this  graph. also we give a relation between the order graph and prime  graph of a group.

In this paper, we study the relationships between graphs and prime spectrum of unitary commutative rings. It is shown that a graph G equipped with G-right topology satisfies some spectral properties. particular give necessarily sufficient condition to obtain graph.

Given a graph G, let G be an oriented graph of G with the orientation σ and skewadjacency matrix S(G). Then the spectrum of S(G) consisting of all the eigenvalues of S(G) is called the skew-spectrum of G, denoted by Sp(G). The skew energy of the oriented graph G, denoted by ES(G), is defined as the sum of the norms of all the eigenvalues of S(G). In this paper, we give orientations of the Krone...