Related papers: Super graphs on groups, II

The commuting graph of a group $G$ is the graph whose vertices are the elements of $G$, two distinct vertices joined if they commute. Our purpose in this paper is twofold: we discuss the computational problem of deciding whether a given…

The eccentricity matrix of a simple connected graph is derived from its distance matrix by preserving the largest non-zero distance in each row and column, while the other entries are set to zero. This article examines the…

In this paper, we study commutative zero-divisor semigroups determined by graphs. We prove a uniqueness theorem for a class of graphs. We show two classes of graphs that have no corresponding semigroups. In particular, any complete graph…

In this paper, we discuss the Hamiltonicity of graphs in terms of Wiener index, hyper-Wiener index and Harary index of their quasi-complement or complement. Firstly, we give some sufficient conditions for an balanced bipartite graph with…

We prove a conjecture of Nadjafi-Arani, Khodashenas and Ashrafi on the difference between the Szeged and Wiener index of a graph. Namely, if $G$ is a 2-connected non-complete graph on $n$ vertices, then $Sz(G)-W(G)\ge 2n-6$. Furthermore,…

The vertices of a $k$-token graph of a graph $G$ correspond to $k$ indistinguishable tokens placed on $k$ different vertices of $G$. Changing some conditions on both the nature of the tokens and the number of tokens allowed in each vertex…

In this paper we introduce the symmetric normaliser graph of a group $G$. The vertex set of this graph consists of elements of the group. Vertices $x$ and $y$ are adjacent if $x$ lies in the normaliser of $\langle y \rangle$ and $y$ lies in…

Let $G$ be a finite group and construct a graph $\Delta(G)$ by taking $G\setminus\{1\}$ as the vertex set of $\Delta(G)$ and by drawing an edge between two vertices $x$ and $y$ if $\langle x,y\rangle$ is cyclic. Let $K(G)$ be the set…

In this paper we first show that among all double-toroidal and triple-toroidal finite graphs only $K_8 \sqcup 9K_1$, $K_8 \sqcup 5K_2$, $K_8 \sqcup 3K_4$, $K_8 \sqcup 9K_3$, $K_8\sqcup 9(K_1 \vee 3K_2)$, $3K_6$ and $3K_6 \sqcup 4K_4 \sqcup…

We associate a graph ${\mathcal N}_{S}$ with a semigroup $S$ (called the upper non-nilpotent graph of $S$). The vertices of this graph are the elements of $S$ and two vertices are adjacent if they generate a semigroup that is not nilpotent…

This paper investigates the relations between modular graph forms, which are generalizations of the modular graph functions that were introduced in earlier papers motivated by the structure of the low energy expansion of genus-one Type II…

For any graph $G$ on $n$ vertices and for any {\em symmetric} subgraph $J$ of $K_{n,n}$, we construct an infinite sequence of graphs based on the pair $(G,J)$. The First graph in the sequence is $G$, then at each stage replacing every…

In this paper, we investigate how the Wiener index of unicyclic graphs varies with graph operations. These results are used to present a sharp lower bound for the Wiener index of unicyclic graphs of order $n$ with girth and the matching…

Le n be any positive integer. A hyperbinary expansion of n is are presentation of n as sum of powers of 2, each power being used at most twice. In this paper we study some properties of a suitable edge-coloured and vertex-weighted oriented…

Comparability graphs are graphs which have transitive orientations. The dimension of a poset is the least number of linear orders whose intersection gives this poset. The dimension ${\rm dim}(X)$ of a comparability graph $X$ is the…

We show that the number of entire maximal graphs with finitely many singular points that are conformally equivalent is a universal constant that depends only on the number of singularities, namely 2^$ for graphs with n+1 singularities. We…

We show that superreflexivity can be characterized in terms of bilipschitz embeddability of word hyperbolic groups. We compare characterizations of superreflexivity in terms of diamond graphs and binary trees. We show that there exist…

We study three mixing properties of a graph: large algebraic connectivity, large Cheeger constant (isoperimetric number) and large spectral gap from 1 for the second largest eigenvalue of the transition probability matrix of the random walk…

We generalize the enhanced power graph by replacing elements with classes under automorphisms. We show that the connectivity and diameter of this graph is similar to that of the enhanced power graph. We consider the universal vertices of…

Let $V$ be a set of cardinality $v$ (possibly infinite). Two graphs $G$ and $G'$ with vertex set $V$ are {\it isomorphic up to complementation} if $G'$ is isomorphic to $G$ or to the complement $\bar G$ of $G$. Let $k$ be a non-negative…