In this paper, we compute a formula for the $a$-number of certain maximal curves given by the equation $y^{q}+y=x^{frac{q+1}{2}}$ over the finite field $mathbb{F}_{q^2}$. The same problem is studied for the maximal curve ...

‎Let $G$ be a graph and $chi^{prime}_{aa}(G)$ denotes the minimum number of colors required for an‎ ‎acyclic edge coloring of $G$ in which no two adjacent vertices are incident to edges colored with the same set of colors‎. ...

Let $R$ be a commutative ring and $M$ an‎ ‎$R$-module‎. ‎In this article‎, ‎we introduce a new generalization of‎ ‎the annihilating-ideal graph of commutative rings to modules‎. ‎The‎ ‎annihilating submodule graph of $M$‎, ...

‎‎In this article‎, ‎for a lattice $mathcal L$‎, ‎we define and investigate‎ ‎the annihilator graph $mathfrak {ag} (mathcal L)$ of $mathcal L$ which contains the zero-divisor graph of $mathcal L$ as a subgraph‎. ‎Also‎, ...

A hypertree is a special type of connected hypergraph that removes‎ ‎any‎, ‎its hyperedge then results in a disconnected hypergraph‎. ‎Relation between hypertrees (hypergraphs) and trees (graphs) can be helpful to solve ...

In this paper, we introduce an approximation for the $k$-nearest neighbor graph ($k$-NNG) on a point set $P$ in $\mathbb{R}^d$. For any given $\varepsilon>0$, we construct a graph, that we call the \emph{approximate $k$-NNG}, ...

Trees are acyclic connected graphs. Plane trees, $d$-ary trees, binary trees, noncrossing trees and their generalizations, which are families of trees, have been enumerated by many authors using various statistics. These ...

Binary array pairs with optimal/ideal correlation values and their algebraic counterparts textquotedblleft difference set pairstextquotedblright;(DSPs) in abelian groups are studied‎. ‎In addition to generalizing known ...

Let $f$ be a proper $k$-coloring of a connected graph $G$ and $Pi=(V_1,V_2,ldots,V_k)$ be an ordered partition of $V(G)$ into the resulting color classes. For a vertex $v$ of $G$, the color code of $v$ with respect to $Pi$ ...

A set $S$ of vertices in a graph $G$ is a dominating set if every‎ ‎vertex of $V-S$ is adjacent to some vertex in $S$‎. ‎The domination‎ ‎number $gamma(G)$ is the minimum cardinality of a dominating set‎ ‎in $G$‎. ‎The ...

‎Metric dimension and defensive $k$-alliance number are two distance-based graph invariants‎ ‎which have applications in robot navigation‎, ‎quantitative analysis of secondary RNA structures‎, ‎national defense and ...

‎‎For a simple connected graph $G$ with $n$ vertices and $m$ edges‎, ‎let $overrightarrow{G}$ be a digraph obtained by giving an arbitrary direction to the edges of $G$‎. ‎In this paper‎, ‎we consider the skew Laplacian/skew ...

A broadcast on a graph $G$ is a function $f‎ : ‎V(G) rightarrow {0‎, ‎1,dots‎, ‎diam(G)}$ such that for every vertex $v in V(G)$‎, ‎$f(v) leq e(v)$‎, ‎where $diam(G)$ is the diameter of $G$‎, ‎and $e(v)$ is the ...

The vertex PI index $PI(G) = sum_{xy in E(G)} [n_{xy}(x)‎ + ‎n_{xy}(y)]$ is a distance-based molecular structure descriptor‎, ‎where $n_{xy}(x)$ denotes the number of vertices which are closer to the vertex $x$ than to the ...

Comer introduced a class of hypergroups, using the name of polygroups. He emphasized the importance of polygroups, by analyzing them in connections to graphs, relations, Boolean and cylindric algebras. Indeed, polygroups ...

The regular graph of ideals of the commutative ring $R$‎, ‎denoted by ${Gamma_{reg}}(R)$‎, ‎is a graph whose vertex‎ ‎set is the set of all non-trivial ideals of $R$ and two distinct vertices $I$ and $J$ are adjacent if ...

For any simple graph $G$, the signless Laplacian matrix of $G$ is defined as $D(G)+A(G)$, where $D(G)$ and $A(G)$ are the diagonal matrix of vertex degrees and the adjacency matrix of $G$, respectively. %Let $\chi(G)$ be ...

In 1991‎, ‎McKay and Radziszowski proved that‎, ‎however each $3$-subset of a $13$-set is assigned one of two colours‎, ‎there is some $4$-subset whose four $3$-subsets have the same colour‎. ‎More than 25 years later‎, ...

The bi-Cayley graph of a finite group $G$ with respect to a subset $Ssubseteq G$‎, ‎which is denoted by $BCay(G,S)$‎, ‎is the graph with‎ ‎vertex set $Gtimes{1,2}$ and edge set ${{(x,1)‎, ‎(sx,2)}mid xin G‎, ‎ sin S}$‎. ...

Given an integer $n\geq4$, how many inequivalent quadrilaterals with ordered integer sides and perimeter $n$ are there? Denoting such number by $Q(n)$, the answer is given by the following closed formula:\[Q(n)=\left\{ ...