Given a planar graph G, we consider drawings of G in the plane where edges are represented by straight line segments (which possibly intersect). Such a drawing is specified by an injective embedding π of the vertex set of G into the plane. Let fix(G, π) be the maximum integer k such that there exists a crossing-free redrawing π of G which keeps k vertices fixed, i.e., there exist k vertices v1,...

the reciprocal degree distance (rdd)‎, ‎defined for a connected graph $g$ as vertex-degree-weighted sum of the reciprocal distances‎, ‎that is‎, ‎$rdd(g) =sumlimits_{u,vin v(g)}frac{d_g(u)‎ + ‎d_g(v)}{d_g(u,v)}.$ the reciprocal degree distance is a weight version of the harary index‎, ‎just as the degree distance is a weight version of the wiener index‎. ‎in this paper‎, ‎we present exact formu...

We enumerate graph homomorphisms to quasi-complete graphs i.e., graphs obtained from complete graphs by removing one edge. The source graphs are complete graphs, quasi-complete graphs, cycles, paths, wheels and broken wheels.

In this paper we prove that the split graphs of 1,n K and are prime cordial graphs. We also show that the square graph of is a prime cordial graph while middle graph of is a prime cordial graph for . Further we prove that the wheel graph admits prime cordial labeling for . , n n B n  , n n B n P 8 4 n 

For any graph F , V (F ) and E (F ) will denote the vertex and edge sets of the p graph F , also let n (F ) = | V (F ) | and e (F ) = | E (F ) | . The graph F  denotes the com lement of F . A graph F will be called a (G , H )−good graph, if F does not contain a ( G and F  does not contain H . Any (G , H )-good graph on n vertices will be called G , H , n )−good graph. The Ramsey number R (G ,...

Penelitian ini bertujuan mengkonstruksi graf dual dari roda (Wn*) dan menentukan bilangan kromatik (Wn*). dimulai menggambarkan beberapa ke , kemudian membangun dengan memanfaatkan graf-graf memberikan warna pada titik-titik dualnya kromatiknya. Diperoleh hasil bahwa Graf merupakan self-dual karena isomorfik yaitu . Pewarnaan titik diperoleh roda, pola kromatik, warna. Berdasarkan penelitian, p...

Steer-By-Wire ( SBW ) has several advantages of packaging flexibility , advanced vehicle control system ,and superior performance . SBW has no mechanical linkage between the steering gear and the steering column. It is possible to control the steering wheel and the front-wheel steering independently. SBW system is composed of two motors controlled by ECU. One motor in the steering wheel is to i...

A graph G = (V,E) is representable if there exists a word W over the alphabet V such that letters x and y alternate in W if and only if (x, y) is in E for each x not equal to y. The motivation to study representable graphs came from algebra, but this subject is interesting from graph theoretical, computer science, and combinatorics on words points of view. In this paper, we prove that for n gre...

A graph is representable if there exists a word over the alphabet such that letters  = , G V E  W V x and alternate in W if and only if y   , x y is in E for each x not equal to . The motivation to study representable graphs came from algebra, but this subject is interesting from graph theoretical, computer science, and combinatorics on words points of view. In this paper, we prove that for...