let $g=(v‎, ‎e)$ be a graph with $p$ vertices and $q$ edges‎. ‎an emph{acyclic‎ ‎graphoidal cover} of $g$ is a collection $psi$ of paths in $g$‎ ‎which are internally-disjoint and cover each edge of the graph‎ ‎exactly once‎. ‎let $f‎: ‎vrightarrow {1‎, ‎2‎, ‎ldots‎, ‎p}$ be a bijective‎ ‎labeling of the vertices of $g$‎. ‎let $uparrow!g_f$ be the‎ ‎directed graph obtained by orienting the...

Hubicka, E.; Syslo, M. M. Minimal bases of a graph. Recent advances in graph theory, Proceedings of 2nd Czechoslovak Symposium on Graph Theory; Fielder, M., Ed.; Academia: Prague, 1975; pp 283-293. Syslo, M. M. On cycle bases of a graph. Networks 1979,9, 123-132. Syslo, M. M. Minimum length cycle bases of a graph. Methods Oper. Res. 1980, 37, 285-290. Kolasinska, E. On a minimum cycle basis of ...

This material consists of 3 parts: 1) Comparison of shadow detection on a challenging case; 2) Applications of our work; 3) Extended visual comparisons of our shadow removal results. We plan to officially release our data set in 2014. To allow for repeatable evaluation for future comparison, our P-code, the user input data, output data and the scripts for ground truth evaluation and quantitativ...

The m-order connectivity index (G) m of a graph G is     1 2 1 1 2 1 ... ... 1 ( ) i i im m v v v i i i m d d d  G where 1 2 1 ... i i im d d d  runs over all paths of length m in G and i d denotes the degree of vertex i v . Also,        1 2 1 1 2 1 ... ... 1 ( ) i i im m v v v i i i ms d d d X G is its m-sum connectivity index. A dendrimer is an artificially manufactured or synth...

Let $M$ be an $R$-module and $0 neq fin M^*={rm Hom}(M,R)$. We associate an undirected graph $gf$ to $M$ in which non-zero elements $x$ and $y$ of $M$ are adjacent provided that $xf(y)=0$ or $yf(x)=0$. Weobserve that over a commutative ring $R$, $gf$ is connected anddiam$(gf)leq 3$. Moreover, if $Gamma (M)$ contains a cycle,then $mbox{gr}(gf)leq 4$. Furthermore if $|gf|geq 1$, then$gf$ is finit...

Let G be a (p,q) graph and A be a group. We denote the order of an element $a in A $ by $o(a).$  Let $ f:V(G)rightarrow A$ be a function. For each edge $uv$ assign the label 1 if $(o(f(u)),o(f(v)))=1 $or $0$ otherwise. $f$ is called a group A Cordial labeling if $|v_f(a)-v_f(b)| leq 1$ and $|e_f(0)- e_f(1)|leq 1$, where $v_f(x)$ and $e_f(n)$ respectively denote the number of vertices labelled w...

in a fictional movie, shadow is not only a technical and thematic concept, but also one of the most illustrative and expressing aesthetic elements of the movie. shadows vast dimensions have led to various discussions and studies along the history of cinema. the main theory of this essay is that a shadow is a comprehensible phenomenon whose interpretation and understanding are greatly essential ...

Shadow detection in real scene images is always a challenging but yet interesting area. Most shadow detection and segmentation methods are based on image analysis. This paper aimed to give a comprehensive and critical study of current shadow detection methods. Various approaches have been discussed related to shadow detection in images. The principles of these methods rely on intensity differen...