Gutman et al. introduced the concepts of energy E (G) and Laplacian energy EL(G) for a simple graph G, and furthermore, they proposed a conjecture that for every graph G, E (G) is not more than EL(G). Unfortunately, the conjecture turns out to be incorrect since Liu et al. and Stevanović et al. constructed counterexamples. However, So et al. verified the conjecture for bipartite graphs. In the ...

Several alternative definitions to graph energy have appeared in literature recently, the first among them being the Laplacian energy, defined by Gutman and Zhou in [Linear Algebra Appl. 414 (2006), 29–37]. We show here that Laplacian energy apparently has small power of discrimination among threshold graphs, by showing that, for each n, there exists a set of n mutually noncospectral connected ...

a spanning tree of graph g is a spanning subgraph of g that is a tree. in this paper, we focusour attention on (n,m) graphs, where m = n, n + 1, n + 2 and n + 3. we also determine somecoefficients of the laplacian characteristic polynomial of fullerene graphs.

Let G be a simple graph with order n and size m. The quantity $$M_1(G)=\sum _{i=1}^{n}d^2_{v_i}$$ is called the first Zagreb index of G, where $$d_{v_i}$$ degree vertex $$v_i$$ , for all $$i=1,2,\dots ,n$$ . signless Laplacian matrix $$Q(G)=D(G)+A(G)$$ A(G) D(G) denote, respectively, adjacency diagonal degrees G. $$q_1\ge q_2\ge \dots \ge q_n\ge 0$$ eigenvalues largest eigenvalue $$q_1$$ spectr...

let $d$ be a digraph with skew-adjacency matrix $s(d)$‎. ‎the skew‎ ‎energy of $d$ is defined as the sum of the norms of all‎ ‎eigenvalues of $s(d)$‎. ‎two digraphs are said to be skew‎ ‎equienergetic if their skew energies are equal‎. ‎we establish an‎ ‎expression for the characteristic polynomial of the skew‎ ‎adjacency matrix of the join of two digraphs‎, ‎and for the‎ ‎respective skew energ...