A necessary and sufficient condition in terms of lower cut sets are given for the insertion of a $gamma-$continuous function between two comparable real-valued functions.

The aim of this paper is to study the properties of t-cut set, strong t-cut set, t-quasi-cut set, strong t-quasi-cut set and ∈ ∨q-cut set of a fuzzy set μ. For any intuitionistic fuzzy A =< μA, νA > and α, β ∈ [0, 1], we define and study the properties of upper (α, β) cut setA(α,β), strong upper (α, β) cut setA(α, β) ̇ , lower (α, β) cut set A, strong lower (α, β) cut set A (α, β) ̇ , upper (α, β...

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 cubic graph G is uniquely edge-3-colorable if G has precisely one 1-factorization. It is proved in this paper, if a uniquely edge-3-colorable, cubic graph G is cyclically 4-edgeconnected, but not cyclically 5-edge-connected, then G must contain a snark as a minor. This is an approach to a conjecture that every triangle free uniquely edge-3-colorable cubic graph must have the Petersen graph as...

In a graph G = ( V , E ), two edges e 1 and 2 are said to have common edge if there exists an ∈ ) different from such that joins vertex of in . That is, 〈 〉 is either P 4 or K 3 A non-empty set D ⊆ open packing no The maximum cardinality the number denoted by ρ o ). this paper, we initiate study on parameter.

Let G = (V, E) be a graph and a weight function w : E -+ Z+. Let T C V be an even subset of the vertices of G. A T-cut is an edge-cutset of the graph which divides T into two odd sets. A T-join is a minimal subset of edges that meets every T-cut (a generalization of solutionS to the Chinese postman problem). The main theorem of this paper gives a tight upper bound on the difference between the ...