We introduce a notion of compatibility for multiplicity matrices. This gives rise to necessary condition the join two (possibly disconnected) graphs G and H be pattern an orthogonal symmetric matrix, or equivalently, minimum number distinct eigenvalues q G∨H equal two. Under additional hypotheses, we show that this is also sufficient. As application, prove q(G∨H) either three when are unions co...

A function ϕ : V ( G )→{1, 2, …, k } of a simple graph is said to be non-inclusive distance vertex irregular -labeling if the sums labels vertices in open neighborhood every are distinct and an inclusive closed each different. The minimum for which has (resp. inclusive) called irregularity strength denoted by d i s ) ). In this paper, join product graphs investigated.

Let $G$ be a connected graph. A set $S$ of vertices in is 1-movable 2-resolving hop dominating if and for every $v \in S$, either $S\backslash \{v\}$ or there exists vertex $u \big((V (G) \backslash S) \cap N_G(v)\big)$ such that $\big(S \{v\}\big) \cup \{u\}$ $G$. The domination number $G$, denoted by $\gamma^{1}_{m2Rh}(G)$ the smallest cardinality In this paper, we investigate concept study i...

In [1], Hamzeh, Iranmanesh Hossein-Zadeh and M. V. Diudea recently introduced the generalized degree distance of graphs. In this paper, we present explicit formulas for this new graph invariant of the Cartesian product, composition, join, disjunction and symmetric difference of graphs and introduce generalized and modified generalized degree distance polynomials of graphs, such that their first...

In this paper, the m-hull sets in the join and composition of two connected graphs are characterized and their m-hull numbers are shown to be direct consequences of these characterizations.

In this paper, some properties of union and join on total regular intuitionistic fuzzy graphs are derived, and also theorems related to these concepts are stated and proved. AMS Mathematics Subject Classification (2010): 03E72, 05C72.

It has recently been observed by Zuiddam that finite graphs form a preordered commutative semiring under the graph homomorphism preorder together with join and disjunctive product as addition multiplication, respectively. This led to new characterization of Shannon capacity $\Theta$ via Strassen's Positivstellensatz: $\Theta(\bar{G}) = \inf_f f(G)$, where $f : \mathsf{Graph} \to \mathbb{R}_+$ r...

The growing size of Semantic Web data expressed in the form of Resource Description Framework (RDF) has made it necessary to develop effective ways of storing this data to save space and to query it in a scalable manner. SPARQL – the query language for RDF data – closely follows SQL syntax. As a natural consequence most of the RDF storage and querying engines are based on modern database storag...