## Abstract

In this paper further result on odd mean labeling is discussed. We prove that the two star *G* = *K*
_{1,m} ∧ *K*
_{1,n} is an odd mean graph if and only if |*m* − *n*| ≤ 3. The condition for a graph to be odd mean is that *p* ≤ *q* + 1, where *p* and *q* stands for the number of the vertices and edges in the graph respectively.

## Abstract

A graph *G* is called supermagic if it admits a labelling of the edges by pairwise di erent consecutive integers such that the sum of the labels of the edges incident with a vertex is independent of the particular vertex. In this paper we will introduce some constructions of supermagic labellings of some graphs generalizing double graphs. Inter alia we show that the double graphs of regular Hamiltonian graphs and some circulant graphs are supermagic.

## Abstract

Häggkvist proved that every 3-regular bipartite graph of order 2*n* with no component isomorphic to the Heawood graph decomposes the complete bipartite graph *K*
_{6n,6n}. In Cichacz and Froncek established a necessary and sufficient condition for the existence of a factorization of the complete bipartite graph *K*
_{n,n} into generalized prisms of order 2*n*. In and Cichacz, Froncek, and Kovar showed decompositions of *K*
_{3n/2,3n/2} into generalized prisms of order 2*n*. In this paper we prove that *K*
_{6n/5,6n/5} is decomposable into prisms of order 2*n* when *n* ≡ 0 (mod 50).

## Abstract

An L(2, 1)-labeling of a graph Γ is an assignment of non-negative integers to the vertices such that adjacent vertices receive labels that differ by at least 2, and those at a distance of two receive labels that differ by at least one. Let λ^{1}
_{2}(Γ) denote the least λ such that Γ admits an L(2, 1)-labeling using labels from {0, 1, . . . , λ}. A Cayley graph of group G is called a circulant graph of order n, if G = Z_{n}. In this paper initially we investigate the upper bound for the span of the L(2, 1)-labeling for Cayley graphs on cyclic groups with “large” connection sets. Then we extend our observation and find the span of L(2, 1)-labeling for any circulants of order n.

## Abstract

In this paper, we compute first Zagreb index (coindex), second Zagreb index (coindex), third Zagreb index, first hyper-Zagreb index, atom-bond connectivity index, fourth atom-bond connectivity index, sum connectivity index, Randić connectivity index, augmented Zagreb index, Sanskruti index, geometric-arithmetic connectivity index and fifth geometric-arithmetic connectivity index of the line graphs of Banana tree graph and Firecracker graph.

## Abstract

In this paper, we study 3–total edge product cordial (3–TEPC) labeling which is a variant of edge product cordial labeling. We discuss Web, Helm, Ladder and Gear graphs in this context of 3–TEPC labeling. We also discuss 3–TEPC labeling of some particular examples with corona graph.

## Abstract

This paper deals with selected theoretical issues pertaining to the setting of asking prices by housing developers. Determinants of the buyer’s and seller’s reservation prices have been identified. The advantages and disadvantages, in terms of behavioral economics, of the pricing strategies practiced by housing developers have been indicated. The strategy based on fixing an asking price roughly equal to the estimated market value of the property was compared with the strategy based on offering an inflated asking price (with the assumption of price negotiations). A second comparison concerned the strategy of price disclosure compared with the strategy of price non-disclosure.

The reflections contained within the article were based on behavioral economics and marketing theory. The discussion was based largely on foreign articles, observed examples of pricing policy carried out by housing developers in Poland, and information obtained from housing developers and real estate brokers who are active on the primary market.

## Abstract

An L(2, 1)-labeling of a graph G = (V,E) is an assignment of nonnegative integers to V such that two adjacent vertices must receive numbers (labels) at least two apart and further, if two vertices are in distance 2 then they receive distinct labels. This article studies a generalization of the L(2, 1)-labeling. We assign sets with at least one element to vertices of G under some conditions.

## Abstract

Let *G* be a graph with vertex set *V* and a distribution of pebbles on the vertices of *V*. A pebbling move consists of removing two pebbles from a vertex and placing one pebble on a neighboring vertex, and a rubbling move consists of removing a pebble from each of two neighbors of a vertex *v* and placing a pebble on *v*. We seek an initial placement of a minimum total number of pebbles on the vertices in *V*, so that no vertex receives more than one pebble and for any given vertex *v* ∈ *V*, it is possible, by a sequence of pebbling and rubbling moves, to move at least one pebble to *v*. This minimum number of pebbles is the 1-restricted optimal rubbling number. We determine the 1-restricted optimal rubbling numbers for Cartesian products. We also present bounds on the 1-restricted optimal rubbling number.

## Abstract

An edge labeling of a connected graph G = (V,E) is said to be local antimagic if it is a bijection f : E → {1, . . . , |E|} such that for any pair of adjacent vertices x and y,f^{+}(x) ≠ f^{+}(y), where the induced vertex label f^{+}(x) = Σf(e), with e ranging over all the edges incident to x. The local antimagic chromatic number of G, denoted by χ_{la}(G), is the minimum number of distinct induced vertex labels over all local antimagic labelings of G. In this paper, several sufficient conditions for χ_{la}(H) ≤ χ_{la}(G) are obtained, where H is obtained from G with a certain edge deleted or added. We then determined the exact value of the local antimagic chromatic number of many cycle-related join graphs.