Let D(G) = (di j)nÃ—n denote the distance matrix of a connected graph G with order n, where di j is equal to the distance between vertices vi and v j in G. A graph is called distance integral if allâ€¦ (More)

In this paper, two results about the signless Laplacian spectral radius q(G) of a graph G of order n with maximum degree âˆ† are proved. Let Bn = K2 + Kn denote a book, i.e., the graph Bn consists of nâ€¦ (More)

The harmonic index H(G) of a graph G is the sum of the weights 2 d(u) + d(v) of all edges uv of G, where d(u) denotes the degree of a vertex u in G. In this work, a lower bound for the harmonic indexâ€¦ (More)

A graph G is called integral if all zeros of the characteristic polynomial P (G, x) are integers. Our purpose is to determine or to characterize which graphs are integral. This problem was posed byâ€¦ (More)

Let M be a mixed graph and [Formula: see text] be its Hermitian-adjacency matrix. If we add a RandiÄ‡ weight to every edge and arc in M, then we can get a new weighted Hermitian-adjacency matrix. Whatâ€¦ (More)

A graph is called integral if all its eigenvalues (of the adjacency matrix) are integers. In this paper, the graphs K1,r â€¢Kn , r âˆ—Kn , K1,r â€¢ Km,n , r âˆ— Km,n and the tree K1,s â€¢ T (q, r,m, t) areâ€¦ (More)

A graph is called integral if all the eigenvalues of its adjacency matrix are integers. In our recent work, we have studied integral complete r-partite graphs Kp1,p2,...,pr = Ka1Â·p1,a2Â·p2,...,asÂ·psâ€¦ (More)

Let âˆ’â†’ G be a digraph and A( âˆ’â†’ G) be the adjacency matrix of âˆ’â†’ G . Let D( âˆ’â†’ G) be the diagonal matrix with outdegrees of vertices of âˆ’â†’ G and Q( âˆ’â†’ G) = D( âˆ’â†’ G) + A( âˆ’â†’ G) be the signlessâ€¦ (More)

Let D(G) = (dij)nÃ—n denote the distance matrix of a connected graph G with order n, where dij is equal to the distance between vertices vi and vj in G. A graph is called distance integral if allâ€¦ (More)