given a non-abelian finite group $g$, let $pi(g)$ denote the set of prime divisors of the order of $g$ and denote by $z(g)$ the center of $g$. thetextit{ prime graph} of $g$ is the graph with vertex set $pi(g)$ where two distinct primes $p$ and $q$ are joined by an edge if and only if $g$ contains an element of order $pq$ and the textit{non-commuting graph} of $g$ is the graph with the vertex s...

The D-eigenvalues {µ1,…,µp} of a graph G are the eigenvalues of its distance matrix D and form its D-spectrum. The D-energy, ED(G) of G is given by ED (G) =∑i=1p |µi|. Two non cospectral graphs with respect to D are said to be D-equi energetic if they have the same D-energy. In this paper we show that if G is an r-regular graph on p vertices with 2r ≤ p - 1, then the complements of iterated lin...

Mathematical chemistry is a branch of theoretical chemistry for discussion and prediction of the molecular structure using mathematical methods without necessarily referring to quantum mechanics. In theoretical chemistry, distance-based molecular structure descriptors are used for modeling physical, pharmacologic, biological and other properties of chemical compounds. The Wiener Polarity index ...

An independent broadcast on a connected graph $G$is a function $f:V(G)to mathbb{N}_0$such that, for every vertex $x$ of $G$, the value $f(x)$ is at most the eccentricity of $x$ in $G$,and $f(x)>0$ implies that $f(y)=0$ for every vertex $y$ of $G$ within distance at most $f(x)$ from $x$.The broadcast independence number $alpha_b(G)$ of $G$is the largest weight $sumlimits_{xin V(G)}f(x)$of an ind...

Department of Computing and Information Technology, Fudan University, Shanghai, China 2 Theoretical Systems Biology Lab , School of Life Science, Fudan University, Shanghai, China Human Genetics Center, University of Texas Health Science Center at Houston, Houston, TX 77225, USA Abstract In recent years, evaluating graph distance has become more and more important in a variety of real applicati...

We show that no more new distance-regular graphs in the tables of book (Brouwer, Cohen, Neumaier, 1989) can be produced by using coset graph additive completely regular codes over finite fields.

Abstract Given a hereditary property of graphs $\mathcal{H}$ and $p\in [0,1]$ , the edit distance function $\textrm{ed}_{\mathcal{H}}(p)$ is asymptotically maximum proportion edge additions plus deletions applied to graph density p sufficient ensure that resulting satisfies . The directly related other well-studied quantities such as speed for -chromatic number random graph. Let be forbidding a...