today, online social networks are very popular due to the possibility of creating relationships between people all over the world. these social networks with possibilities such as friend recommendation generally use local features derived from social graph structure. for friend recommendation, there are different algorithms with local and global approaches. in this paper, we proposed an algorit...

In this study, the explicit expressions for F-index and coindex of derived graphs such as a line graph, subdivision graph, vertex-semitotal graph, edge-semitotal graph, total graph and paraline graph (line graph of the subdivision graph) are obtained.

let $r$ be a commutative ring with identity. let $g(r)$ denote the maximal graph associated to $r$, i.e., $g(r)$ is a graph with vertices as the elements of $r$, where two distinct vertices $a$ and $b$ are adjacent if and only if there is a maximal ideal of $r$ containing both. let $gamma(r)$ denote the restriction of $g(r)$ to non-unit elements of $r$. in this paper we study the various graphi...

This paper introduces a general framework for defining the entropy of a graph. Our definition is based on a local information graph and on information functionals derived from the topological structure of a given graph. More precisely, an information functional quantifies structural information of a graph based on a derived probability distribution. Such a probability distribution leads directl...

In this paper, a novel beam alignment algorithm based on the sparse graph coding theory is proposed for millimeter wave (mmWave) time-varying channels. Firstly, pilot design method introduced to transform mmWave into sparse-graph and detection problem. Inspired by Low-Density-Parity-Check (LDPC) codes fountain codes, multi-stage of measurement matrix theoretical bound probability success derive...

In this note, we obtain the expressions for multiplicative Zagreb indices and coindices of derived graphs such as a line graph, subdivision graph, vertex-semitotal graph, edge-semitotal graph, total graph and paraline graph.

Semantic graph representation of text is an important part of natural language processing applications such as text summarisation. We have studied two ways of constructing the semantic graph of a document from dependency parsing of its sentences. The first graph is derived from the subject-object-verb representation of sentence, and the second graph is derived from considering more dependency r...

This work defines the concepts of strong efficient dominating set and intuitionistic fuzzy graph. We also introduce an graph a number graphs. The dominant in graphs has some limitations that are studied, derived..

‎let $d_{n,m}=big[frac{2n+1-sqrt{17+8(m-n)}}{2}big]$ and‎ ‎$e_{n,m}$ be the graph obtained from a path‎ ‎$p_{d_{n,m}+1}=v_0v_1 cdots v_{d_{n,m}}$ by joining each vertex of‎ ‎$k_{n-d_{n,m}-1}$ to $v_{d_{n,m}}$ and $v_{d_{n,m}-1}$‎, ‎and by‎ ‎joining $m-n+1-{n-d_{n,m}choose 2}$ vertices of $k_{n-d_{n,m}-1}$‎ ‎to $v_{d_{n,m}-2}$‎. ‎zhang‎, ‎liu and zhou [on the maximal eccentric‎ ‎connectivity ind...

the order graph of a group $g$, denoted by $gamma^*(g)$, is a graph whose vertices are subgroups of $g$ and two distinct vertices $h$ and $k$ are adjacent if and only if $|h|big{|}|k|$ or $|k|big{|}|h|$. in this paper, we study the connectivity and diameter of this  graph. also we give a relation between the order graph and prime  graph of a group.