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...

Let G = (V,E) be a graph of order n. A distance magic labeling of G is a bijection l : V → {1, 2, . . . , n} for which there exists a positive integer k such that ∑ x∈N(v) l(x) = k for all v ∈ V , where N(v) is the open neighborhood of v. In this paper we deal with circulant graphs C(1, p). The circulant graph Cn(1, p) is the graph on the vertex set V = {x0, x1, . . . , xn−1} with edges (xi, xi...

We present an algorithm for the parameterized feedback vertex set problem that runs in time O((2 lg k + 2 lg lg k + 18)n). This improves the previous O(max{12, (4 lg k)}n) algorithm by Raman et al. by roughly a 2 factor (n ∈ O(n) is the time needed to multiply two n × n matrices). Our results are obtained by developing new combinatorial tools and employing results from extremal graph theory. We...

Since the b ghost in the pure spinor formalism is a composite operator depending on non-minimal variables, it is not trivial to impose the Siegel gauge condition b0V = 0 on BRST-invariant vertex operators. Using the antifield vertex operator V ∗ of ghost-number +2, we show that Siegel gauge unintegrated vertex operators can be constructed as b0V ∗ and Siegel gauge integrated vertex operators as...

An injective function f : V (G)→ {0, 1, 2, . . . , q} is an odd sum labeling if the induced edge labeling f∗ defined by f∗(uv) = f(u) + f(v), for all uv ∈ E(G), is bijective and f∗(E(G)) = {1, 3, 5, . . . , 2q − 1}. A graph is said to be an odd sum graph if it admits an odd sum labeling. In this paper, we have studied the odd sum property of the subdivision of the triangular snake, quadrilatera...

The line graph of G, denoted L(G), is the graph with vertex set E(G), where vertices x and y are adjacent in L(G) iff edges x and y share a common vertex in G. In this paper, we determine all graphs G for which L(G) is a circulant graph. We will prove that if L(G) is a circulant, then G must be one of three graphs: the complete graph K4, the cycle Cn, or the complete bipartite graph Ka,b, for s...

A weighting of vertices of a graph is admissible if there exists an edge weighting such that the weight of each vertex equals the sum of weights of its incident edges. Given an admissible vertex weighting of a graph, an invariant set is an edge set such that the sum of the weights of its edges is the same for every edge weighting, and a nonempty invariant set is minimal if none of its nonempty ...

A cograph completion of an arbitrary graph G is a cograph supergraph of G on the same vertex set. Such a completion is called minimal if the set of edges added to G is inclusion minimal. In this paper we present two results on minimal cograph completions. The first is a a characterization that allows us to check in linear time whether a given cograph completion is minimal. The second result is ...

A cograph completion of an arbitrary graph G is a cograph supergraph of G on the same vertex set. Such a completion is called minimal if the set of edges added to G is inclusion minimal. In this paper we present two results on minimal cograph completions. The first is a a characterization that allows us to check in linear time whether a given cograph completion is minimal. The second result is ...