Note on edge irregular reflexive labelings of graphs

Irregular labelings of circulant graphs

([3]) and tvs(G) ≤ ⌈ 3n δ ⌉ + 1 ([1]). The exact values for some families of graphs are also known, e.g. the value of s(Cin(1, k), given in [2]. We prove that tvs(Cin(1, 2, . . . , k)) = n+2k 2k+1 , while s(Cin(1, 2, . . . , k)) = n+2k−1 2k . In order to do that, we split the graph Cin(1, 2, . . . , k) into segments and label each segment using 0, 1 and 2 in such a way that the weighted degrees...

A note on vertex-edge Wiener indices of graphs

The vertex-edge Wiener index of a simple connected graph G is defined as the sum of distances between vertices and edges of G. Two possible distances D_1(u,e|G) and D_2(u,e|G) between a vertex u and an edge e of G were considered in the literature and according to them, the corresponding vertex-edge Wiener indices W_{ve_1}(G) and W_{ve_2}(G) were introduced. In this paper, we present exact form...

note on edge distance-balanced graphs

edge distance-balanced graphs are graphs in which for every edge $e = uv$ the number of edges closer to vertex $u$ than to vertex $v$ is equal to the number of edges closer to $v$ than to $u$. in this paper, we study this property under some graph operations.

On edge-magic labelings of certain disjoint unions of graphs

a note on vertex-edge wiener indices of graphs

the vertex-edge wiener index of a simple connected graph g is defined as the sum of distances between vertices and edges of g. two possible distances d_1(u,e|g) and d_2(u,e|g) between a vertex u and an edge e of g were considered in the literature and according to them, the corresponding vertex-edge wiener indices w_{ve_1}(g) and w_{ve_2}(g) were introduced. in this paper, we present exact form...