the set of all non-increasing non-negative integer sequences $pi=(d_1‎, ‎d_2,ldots,d_n)$ is denoted by $ns_n$‎. ‎a sequence $piin ns_{n}$ is said to be graphic if it is the degree sequence of a simple graph $g$ on $n$ vertices‎, ‎and such a graph $g$ is called a realization of $pi$‎. ‎the set of all graphic sequences in $ns_{n}$ is denoted by $gs_{n}$‎. ‎the complete product split graph on $l‎ ...

‎The distinguishing number (resp. index) $D(G)$ ($D'(G)$) of a graph $G$ is the least integer $d$‎ ‎such that $G$ has an vertex labeling (resp. edge labeling) with $d$ labels that is preserved only by a trivial‎ ‎automorphism‎. ‎For any $n in mathbb{N}$‎, ‎the $n$-subdivision of $G$ is a simple graph $G^{frac{1}{n}}$ which is constructed by replacing each edge of $G$ with a path of length $n$...

In shadow volume rendering, the shadow volume silhouette edges are used to create primitives that model the shadow volume. A common misconception is that the vertices on such silhouettes can only be connected to two silhouette edges, i.e., have degree two. Furthermore, some believe that the degree of such a vertex can have any degree. In this short note, we present a geometric proof that shows ...

Does an assimilative illusion like the Delboeuf illusion occur in the human face? We investigated factors that might influence the perceived size of the eyes in a realistic face. Experiment 1 manipulated the position of the eyebrows (high or low), the presence/absence of eye shadow, and the viewing distance (0.6 m or 5 m), then measured the perceived eye size using a psychophysical method. The ...

The concept of super line graph was introduced in the year 1995 by Bagga, Beineke and Varma. Given a graph with at least r edges, the super line graph of index r, Lr(G), has as its vertices the sets of r-edges of G, with two adjacent if there is an edge in one set adjacent to an edge in the other set. The line completion number lc(G) of a graph G is the least positive integer r for which Lr(G) ...

a graph $g$ is called a fractional‎ ‎$(k,n',m)$-critical deleted graph if any $n'$ vertices are removed‎ ‎from $g$ the resulting graph is a fractional $(k,m)$-deleted‎ ‎graph‎. ‎in this paper‎, ‎we prove that for integers $kge 2$‎, ‎$n',mge0$‎, ‎$nge8k+n'+4m-7$‎, ‎and $delta(g)ge k+n'+m$‎, ‎if‎ ‎$$|n_{g}(x)cup n_{g}(y)|gefrac{n+n'}{2}$$‎ ‎for each pair of non-adjac...

In this paper, we use the concept of graph convergence of H(.,.)-co-accretive mapping introduced by [R. Ahmad, M. Akram, M. Dilshad, Graph convergence for the H(.,.)-co-accretive mapping with an application, Bull. Malays. Math. Sci. Soc., doi: 10.1007/s40840-014-0103-z, 2014$] and define an over-relaxed proximal point method to obtain the solution of a generalized variational inclusion problem ...

We propose a method for measuring the black hole charge by imaging a black hole shadow in a galactic center by future interferometers. Even when the black hole is uncharged, it is possible to confirm the charge neutrality by this method. We first derive the analytic formulae of the black hole shadow in an optically thin medium around a charged spinning black hole, and then investigate how conto...

let $g$ be an $(n,m)$-graph. we say that $g$ has property $(ast)$if for every pair of its adjacent vertices $x$ and $y$, thereexists a vertex $z$, such that $z$ is not adjacentto either $x$ or $y$. if the graph $g$ has property $(ast)$, thenits complement $overline g$ is connected, has diameter 2, and itswiener index is equal to $binom{n}{2}+m$, i.e., the wiener indexis insensitive of any other...

For any $k in mathbb{N}$, the $k$-subdivision of graph $G$ is a simple graph $G^{frac{1}{k}}$, which is constructed by replacing each edge of $G$ with a path of length $k$. In [Moharram N. Iradmusa, On colorings of graph fractional powers, Discrete Math., (310) 2010, No. 10-11, 1551-1556] the $m$th power of the $n$-subdivision of $G$ has been introduced as a fractional power of $G$, denoted by ...