In the extension of irregularity indices, Abdo et. al. [1] defined the total irregu-larity of a graph G = (V, E) as irrt(G) = 21 Pu,v∈V (G) du − dv, where du denotesthe vertex degree of a vertex u ∈ V (G). In this paper, we investigate the totalirregularity of trees with bounded maximal degree Δ and state integer linear pro-gramming problem which gives standard information about extremal trees a...

For any vertex v and any edge e in a non-trivial connected graph G, the distance sum d(v) of v is d(v) = ∑ u∈V d(v, u), the vertex-to-edge distance sum d1(v) of v is d1(v) = ∑ e∈E d(v, e), the edge-to-vertex distance sum d2(e) of e is d2(e) = ∑ v∈V d(e, v) and the edge-to-edge distance sum d3(e) of e is d3(e) = ∑ f∈E d(e, f). The set M(G) of all vertices v for which d(v) is minimum is the media...

 The a im of th is paper was to study the effects w hey pro t e in c oat i ng on ch e m ic al a nd physic al properties of gut t ed K i l ka dur i ng f roz en stor a ge. Coating of Kilka has done by dipping in whey protein solution with different concentrations of 3, 7, 10 and 13%, for 1h. Then, after being packed in polyethylene dishes, they were covered in cellophane blanket and stored in -18...

Let G^s be a signed graph, where G = (V;E) is the underlying simple graph and s : E(G) to {+, -} is the sign function on E(G). In this paper, we obtain k-th signed spectral moment and k-th signed Laplacian spectral moment of Gs together with coefficients of their signed characteristic polynomial and signed Laplacian characteristic polynomial are calculated.

For a graph G, the irregularity and total irregularity of G are defined as irr(G)=∑_(uv∈E(G))〖|d_G (u)-d_G (v)|〗 and irr_t (G)=1/2 ∑_(u,v∈V(G))〖|d_G (u)-d_G (v)|〗, respectively, where d_G (u) is the degree of vertex u. In this paper, we characterize all ‎connected Eulerian graphs with the second minimum irregularity, the second and third minimum total irregularity value, respectively.

Let G be a (p,q) graph. An injective map f : E(G) → {±1,±2,...,±q} is said to be an edge pair sum labeling if the induced vertex function f*: V (G) → Z - {0} defined by f*(v) = ΣP∈Ev f (e) is one-one where Ev denotes the set of edges in G that are incident with a vertex v and f*(V (G)) is either of the form {±k1,±k2,...,±kp/2} or {±k1,±k2,...,±k(p-1)/2} U {±k(p+1)/2} according as p is even or o...

Given an undirected graph G = (V,E), an edge cost c(e) ≥ 0 for each edge e ∈ E, a vertex prize p(v) ≥ 0 for each vertex v ∈ V , and an edge budget B. The budget prize collecting tree problem is to find a subtree T ′ = (V ′, E′) that maximizes ∑ v∈V ′ p(v), subject to ∑ e∈E′ c(e) ≤ B. We present a (4 + 2)-approximation algorithm.