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...

A cocomparability graph is a graph whose complement admits a transitive orientation. An interval graph is the intersection graph of a family of intervals on the real line. In this paper we investigate the relationships between interval and cocomparability graphs. This study is motivated by recent results [5, 13] that show that for some problems, the algorithm used on interval graphs can also be...

A graph is radially maximal if its radius decreases after the addition of any edge of its complement. It is proved that any graph can be an induced subgraph of a regular radially maximal graph with a prescribed radius T 2: 3. For T 2: 4, k 2: 1, radially maximal graphs with radius T containing k cut-nodes are constructed.

A geometric graph is a labeled graph whose vertices are points in the 2D plane with an isomorphism invariant under geometric transformations such as translation, rotation, and scaling. While Kuramochi and Karypis (ICDM2002) extensively studied the frequent pattern mining problem for geometric subgraphs, the maximal graph mining has not been considered so far. In this paper, we study the maximal...

A geometric graph is a labeled graph whose vertices are points in the 2D plane with isomorphism invariant under geometric transformations such as translation, rotation, and scaling. While Kuramochi and Karypis (ICDM2002) extensively studied the frequent pattern mining problem for geometric subgraphs, the maximal graph mining has not been considered so far. In this paper, we study the maximal (o...

An induced matching in a graph is a set of edges whose endpoints induce a 1-regular subgraph. It is known that every n-vertex graph has at most 10 ≈ 1.5849 maximal induced matchings, and this bound is best possible. We prove that every n-vertex triangle-free graph has at most 3 ≈ 1.4423 maximal induced matchings, and this bound is attained by every disjoint union of copies of the complete bipar...

Let G be a finite group of even order v. Does there exist a 1−factorization of Kv admitting G as an automorphism group acting sharply transitively on vertices? If G is cyclic and v = 2, for t ≥ 3, then the answer to the previous question is known to be negative by a result of A.Hartman and A.Rosa (1985). For several large families of groups of even order constructions have always been found thu...

A basic statement in graph theory is that every inclusion-maximal forest is connected, i.e. a tree. Using a definiton for higher dimensional forests by Graham and Lovász and the connectivity-related notion of tightness for hypergraphs introduced by Arocha, Bracho and Neumann-Lara in, we provide an example of a saturated, i.e. inclusion-maximal 3-forest that is not tight. This resolves an open p...