It is shown that the graphs for which the Szeged index equals‖ G‖⋅∣ G∣ 24 are
precisely connected, bipartite, distance-balanced graphs. This enables us to disprove a …

In this paper, we investigate various algebraic and graph theoretic properties of the distance
matrix of a graph. Two graphs are D-cospectral if their distance matrices have the same …

The status of a vertex u, denoted by σ G (u), is the sum of the distances between u and all
other vertices in a graph G. The first and second status connectivity indices of a graph G are …

Given a graph G and a set X⊆ V (G), the relative Wiener index of X in G is defined as WX
(G)=∑{u, v}∈ X 2 d G (u, v). The graphs G (of even order) in which for every partition V (G) …

The signless Laplacian reciprocal distance matrix for a simple connected graph G is defined
as RQ (G)= diag (RH (G))+ RD (G). Here, RD (G) is the Harary matrix (also called reciprocal …

A graph Γ is distance-balanced if for each pair u, v of adjacent vertices of Γ the number of
vertices closer to u than to v is equal to the number of vertices closer to v than to u. Apart …

A nonempty graph Γ is called nicely distance-balanced, whenever there exists a positive
integer γ Γ, such that for any two adjacent vertices u, v of Γ there are exactly γ Γ vertices of Γ …

If G is a graph, and if for e= uv∈ E (G) the number of vertices closer to u than to v is denoted
by nu, then Mo (G)= Σ uv∈ E (G)| nu-nv| is the Mostar index of G. In this paper, the Mostar …

An unweighted comma connected graph is distance hyphen balanced open parenthesis
also called se lf hyphen median closing parenthesis if there exists a number d such that …

A connected graph Γ is said to be distance-balanced whenever for any pair of adjacent
vertices u, v of Γ the number of vertices closer to u than to v is equal to the number of vertices …