In the graph distance game, two players alternate in constructing a maximal path. The objective function is the distance between the two endpoints of the path, which one player tries to maximize and the other tries to minimize. In this paper we examine the distance game for various graph operations: the join, the corona and the lexicographic product of graphs. We provide general bounds and exac...

A graph is said to be cordial if it has 0 - 1 labeling which satisfies particular conditions. In this paper, we construct the corona between paths and second power of fan graphs explain necessary sufficient conditions for construction cordial.

let g be a (p, q) graph. let k be an integer with 2 ≤ k ≤ p and f from v (g) to the set {1, 2, . . . , k} be a map. for each edge uv, assign the label |f(u) − f(v)|. the function f is called a k-difference cordial labeling of g if |νf (i) − vf (j)| ≤ 1 and |ef (0) − ef (1)| ≤ 1 where vf (x) denotes the number of vertices labelled with x (x ∈ {1, 2 . . . , k}), ef (1) and ef (0) respectively den...

introduction: food industry is one of the most important industries in developing countries that has an enormous role in employment, export and value added of the agricultural sector. iran as a developing country has a comparative advantage in food product industries for several reasons such as adequate and cheap raw materials and having several companies in the field of food industries. the fo...

We define a total k-labeling φ of graph G as combination an edge labeling φe:E(G)→{1,2,…,ke} and vertex φv:V(G)→{0,2,…,2kv}, such that φ(x)=φv(x) if x∈V(G) φ(x)=φe(x) x∈E(G), where k= max {ke,2kv}. The is called irregular reflexive every two different edges has distinct weights, the weight defined summation label itself its labels. Thus, smallest value k for which strength G. In this paper, we ...