Bipolar fuzzy graph (BFG) coloring techniques are used to solve many complex real world problems. The chromatic number of complement BFG is obtained and compared with the corresponding BFGs. This paper an attempt define in a based on strong edges. complete BF tree obtained.

Let F be a fixed field and let X simplicial complex on the vertex set V. The Leray number L ( ; ) is minimal d such that for all i ⩾ S ⊂ V , induced [ ] satisfies H ∼ = 0 . numbers play role in formulating proving topological Helly-type theorems. For two complexes Y same V, define relative as ∖ τ ∈ In this paper we extend colorful Helly theorem to setting. Our main tool spectral sequence inters...

The chromatic sum of a graph G, ∑ (G), is introduced in the dissertation of Kubicka [3]. It is defined as the smallest possible total over all vertices that can occur among all colorings of G using natural numbers for the colors. It is known that computing the chromatic sum of an arbitrary graph is an NP-complete problem. The vertex-strength of the graph G, denoted by s(G), is the smallest inte...

Fuzzy set theory is applied to quantify the non-probabilistic uncertainty alternatively termed as epistemic uncertainty. An algorithm “Fuzzy Centered Radius” has been developed for quantification of epistemic uncertainty. Uncertainty analysis is also carried out using fuzzy vertex method. Analytical solution of one dimension heat conduction and numerical solution of heat removal from circular f...

In this paper d2 degree of a vertex and total d2 -degree of a vertex in an intuitionistic fuzzy graphs are defined. Also (2, (c1, c2))-regularity and totally (2, (c1, c2))-regularity of an intuitionistic fuzzy graphs are defined. A relation between (2, (c1, c2))-regularity and totally (2, (c1, c2))-regularity on intuitionistic fuzzy graph is studied. (2, (c1, c2))regularity on a path on four ve...

In 2004, G. Ganesan and C. Raghavendra Rao introduced the concept of Rough Fuzzy Groups. In this paper, we have adapted this approach in defining the algebraic closure of a given fuzzy graph using each vertex.

Let P1, . . . , Pd+1 ⊂ R be d-dimensional point sets such that the convex hull of each Pi contains the origin. We call the sets Pi color classes, and we think of the points in Pi as having color i. A colorful choice is a set with at most one point of each color. The colorful Carathéodory theorem guarantees the existence of a colorful choice whose convex hull contains the origin. So far, the com...

Since the proof of a "colorful" version [Caratheodory's theorem](https://en.wikipedia.org/wiki/Carath%C3%A9odory%27s_theorem_%28convex_hull%29) by Bárány in 1982, it has been an important problem to obtain colorful extensions other classical results discrete geometry (for instance Tverberg's theorem). The present paper continues this line research, but context extremal graph theory rather than ...

The Colorful Motif problem asks if, given a vertex-colored graph G, there exists a subset S of vertices of G such that the graph induced by G on S is connected and contains every color in the graph exactly once. The problem is motivated by applications in computational biology and is also well-studied from the theoretical point of view. In particular, it is known to be NPcomplete even on trees ...