Let G be a (molecular) graph with n vertices, and di be the degree of its i-th vertex. Then, the inverse sum indeg matrix of G is the n×n matrix C(G) with entries cij=didjdi+dj, if the i-th and the j-th vertices are adjacent and 0 otherwise. Let μ1≥μ2≥…≥μn be the eigenvalues of C arranged in order. The inverse sum indeg energy of G, εisi(G) can be represented as ∑j=1n|μi|. In this paper, we establish several novel upper and lower sharp bounds on μ1 and εisi(G) via some other graph parameters, and describe the structures of the extremal graphs
AbstractFor a given simple graph G, the energy of G, denoted by E(G), is defined as the sum of the a...
Let G be a simple undirected graph of order n with vertex set V(G) ={v1, v2, ..., vn}. Let di be the...
Given a complex m × n matrix A, we index its singular values as σ1 (A) ≥ σ2 (A) ≥ ⋯ and call the val...
Let G be a (molecular) graph with n vertices, and di be the degree of its i-th vertex. Then, the inv...
Let G = (V,E) be a simple connected graph with the vertex set V = {1,2,...,n} and sequence of vertex...
The inverse sum indeg index I S I (G) of a simple graph G is defined as the sum of the terms d G (u)...
Let G be a graph on n vertices and m edges, with maximum degree Δ(G) and minimum degree δ(G). Let A ...
Let G be a finite simple undirected graph with n vertices and m edges. The energy of a graph G , den...
Let G be a simple graph of order n. The energy E(G) of G is the sum of the absolute values of the e...
Let G be a finite simple undirected graph with n vertices and m edges. For v ∈ V, the 2-degree of v ...
In this paper, we give two upper bounds for the extended energy of a graph one in terms of ordinary ...
For a graph $G$ the degree sum adjacency matrix $DS_A(G)$ is defined as a matrix, in which every ele...
The 2-degree of vi, denoted by ti, is the sum of degrees of the vertices adjacent to vi, 1 i n. Le...
AbstractLet G be a graph on n vertices, and let λ1,λ2,…,λn be the eigenvalues of a (0,1)-adjacency m...
We use a lemma due to Fiedler to obtain eigenspaces of some graphs and apply these results to graph ...
AbstractFor a given simple graph G, the energy of G, denoted by E(G), is defined as the sum of the a...
Let G be a simple undirected graph of order n with vertex set V(G) ={v1, v2, ..., vn}. Let di be the...
Given a complex m × n matrix A, we index its singular values as σ1 (A) ≥ σ2 (A) ≥ ⋯ and call the val...
Let G be a (molecular) graph with n vertices, and di be the degree of its i-th vertex. Then, the inv...
Let G = (V,E) be a simple connected graph with the vertex set V = {1,2,...,n} and sequence of vertex...
The inverse sum indeg index I S I (G) of a simple graph G is defined as the sum of the terms d G (u)...
Let G be a graph on n vertices and m edges, with maximum degree Δ(G) and minimum degree δ(G). Let A ...
Let G be a finite simple undirected graph with n vertices and m edges. The energy of a graph G , den...
Let G be a simple graph of order n. The energy E(G) of G is the sum of the absolute values of the e...
Let G be a finite simple undirected graph with n vertices and m edges. For v ∈ V, the 2-degree of v ...
In this paper, we give two upper bounds for the extended energy of a graph one in terms of ordinary ...
For a graph $G$ the degree sum adjacency matrix $DS_A(G)$ is defined as a matrix, in which every ele...
The 2-degree of vi, denoted by ti, is the sum of degrees of the vertices adjacent to vi, 1 i n. Le...
AbstractLet G be a graph on n vertices, and let λ1,λ2,…,λn be the eigenvalues of a (0,1)-adjacency m...
We use a lemma due to Fiedler to obtain eigenspaces of some graphs and apply these results to graph ...
AbstractFor a given simple graph G, the energy of G, denoted by E(G), is defined as the sum of the a...
Let G be a simple undirected graph of order n with vertex set V(G) ={v1, v2, ..., vn}. Let di be the...
Given a complex m × n matrix A, we index its singular values as σ1 (A) ≥ σ2 (A) ≥ ⋯ and call the val...