Graph theory is a very natural and powerful tool in combinatorial operations research. Some important operations research problems particularly inventory control problem that can be solved using graphs. A brief review of graph theory applications to problems of inventory systems are made in this paper. It suggests the possibilities which exist for improving the operational, tactical and strateg...

X iv :1 70 4. 01 92 2v 1 [ m at h. C O ] 6 A pr 2 01 7 Sandwiches Missing Two Ingredients of Order Four José D. Alvarado Simone Dantas Dieter Rautenbach 1 Instituto de Matemática e Estat́ıstica, Universidade Federal Fluminense, Niterói, Brazil [email protected], [email protected] 2 Institute of Optimization and Operations Research, Ulm University, Ulm, Germany dieter.rautenbach@uni-ul...

The ``height'' of a graph G is defined to be the number of steps to construct G by two simple graph operations. Let Bn be the graph obtained from an n-edge path by doubling each edge in parallel. Then, for any minor-closed class G of graphs, the following are proved to be equivalent: (1) Some Bn is not in G; (2) There is a number h such that every graph in G has height at most h; (3) G is well-...

In this paper we introduce two new operations on graphs: sum and union corresponding to parallel and series operation respectively. We determine N -free graph as the graph that does not embed Necklace 4. We define “fin RelStr” as the set of all graphs with finite carriers. We also define the smallest class of graphs which contains the one-element graph and which is closed under parallel and ser...

The hyper-Zagreb index of a connected graph G, denoted by HM(G), is defined as HM(G) = ∑ uv∈E(G) [dG(u) + dG(v)] where dG(z) is the degree of a vertex z in G. In this paper, we study the hyper-Zagreb index of four operations on graphs.

For k = 0, 1, 2, 3, 4, 5, let Pk be the class of k-edge-connected 5regular planar graphs. In this paper, graph operations are introduced that generate all graphs in each Pk. ∗Research partially supported by NSF grants DMS-0556091 and ITR-0326387. †Research partially supported by Board of Regents grant LEQSF(2004-07)-RD-A-22.