Bounds on the Distance Energy and the Distance Estrada Index of Strongly Quotient Graphs

A Note on Strongly Quotient Graphs

Albertson energy and Albertson Estrada index of graphs

‎Let $G$ be a graph of order $n$ with vertices labeled as $v_1‎, ‎v_2,dots‎ , ‎v_n$‎. ‎Let $d_i$ be the degree of the vertex $v_i$ for $i = 1‎, ‎2‎, ‎cdots‎ , ‎n$‎. ‎The Albertson matrix of $G$ is the square matrix of order $n$ whose $(i‎, ‎j)$-entry is equal to $|d_i‎ - ‎d_j|$ if $v_i $ is adjacent to $v_j$ and zero‎, ‎otherwise‎. ‎The main purposes of this paper is to introduce the Albertson ...

Sharp Upper bounds for Multiplicative Version of Degree Distance and Multiplicative Version of Gutman Index of Some Products of Graphs

In $1994,$ degree distance  of a graph was introduced by Dobrynin, Kochetova and Gutman. And Gutman proposed the Gutman index of a graph in $1994.$ In this paper, we introduce the concepts of  multiplicative version of degree distance and the multiplicative version of Gutman index of a graph. We find the sharp upper bound for the  multiplicative version of degree distance and multiplicative ver...

On Complementary Distance Signless Laplacian Spectral Radius and Energy of Graphs

Let $D$ be a diameter and $d_G(v_i, v_j)$ be the distance between the vertices $v_i$ and $v_j$ of a connected graph $G$. The complementary distance signless Laplacian matrix of a graph $G$ is $CDL^+(G)=[c_{ij}]$ in which $c_{ij}=1+D-d_G(v_i, v_j)$ if $ineq j$ and $c_{ii}=sum_{j=1}^{n}(1+D-d_G(v_i, v_j))$. The complementary transmission $CT_G(v)$ of a vertex $v$ is defined as $CT_G(v)=sum_{u in ...

Product version of reciprocal degree distance of composite graphs

A {it topological index} of a graph is a real number related to the graph; it does not depend on labeling or pictorial representation of a graph. In this paper, we present the upper bounds for the product version of reciprocal degree distance of the tensor product, join and strong product of two graphs in terms of other graph invariants including the Harary index and Zagreb indices.