نتایج جستجو برای: degree of vertex
تعداد نتایج: 21170588 فیلتر نتایج به سال:
for a graph $g$ with edge set $e(g)$, the multiplicative sum zagreb index of $g$ is defined as$pi^*(g)=pi_{uvin e(g)}[d_g(u)+d_g(v)]$, where $d_g(v)$ is the degree of vertex $v$ in $g$.in this paper, we first introduce some graph transformations that decreasethis index. in application, we identify the fourteen class of trees, with the first through fourteenth smallest multiplicative sum zagreb ...
for a graph $g$ with edge set $e(g)$, the multiplicative second zagreb index of $g$ is defined as $pi_2(g)=pi_{uvin e(g)}[d_g(u)d_g(v)]$, where $d_g(v)$ is the degree of vertex $v$ in $g$. in this paper, we identify the eighth class of trees, with the first through eighth smallest multiplicative second zagreb indeces among all trees of order $ngeq 14$.
We investigate the degree distribution resulting from graph generation models based on rank-based attachment. In rank-based attachment, all vertices are ranked according to a ranking scheme. The link probability of a given vertex is proportional to its rank raised to the power −α, for some α ∈ (0, 1). Through a rigorous analysis, we show that rank-based attachment models lead to graphs with a p...
Let $G$ be a finite group and $pi_{e}(G)$ be the set of orders of all elements in $G$. The set $pi_{e}(G)$ determines the prime graph (or Grunberg-Kegel graph) $Gamma(G)$ whose vertex set is $pi(G)$, the set of primes dividing the order of $G$, and two vertices $p$ and $q$ are adjacent if and only if $pqinpi_{e}(G)$. The degree $deg(p)$ of a vertex $pin pi(G)$, is the number of edges incident...
the gutman index and degree distance of a connected graph $g$ are defined as begin{eqnarray*} textrm{gut}(g)=sum_{{u,v}subseteq v(g)}d(u)d(v)d_g(u,v), end{eqnarray*} and begin{eqnarray*} dd(g)=sum_{{u,v}subseteq v(g)}(d(u)+d(v))d_g(u,v), end{eqnarray*} respectively, where $d(u)$ is the degree of vertex $u$ and $d_g(u,v)$ is the distance between vertices $u$ and $v$. in th...
an extended star is a tree which has only one vertex with degree larger than two. the -center problem in a graph asks to find a subset of the vertices of of cardinality such that the maximum weighted distances from to all vertices is minimized. in this paper we consider the -center problem on the unweighted extended stars, and present some properties to find solution.
two groups of students were assigned as experimental and control ones, and were given instruction on directed reading-thinking activities and after some treatment, they were post-tested. although the initial pre-test did not show any significant differences, the final post-test result revealed that the cooperative reading comprehension helped the experimental group. the cooperative students’...
the harmonic index of a connected graph $g$, denoted by $h(g)$, is defined as $h(g)=sum_{uvin e(g)}frac{2}{d_u+d_v}$ where $d_v$ is the degree of a vertex $v$ in g. in this paper, expressions for the harary indices of the join, corona product, cartesian product, composition and symmetric difference of graphs are derived.
the inflation $g_{i}$ of a graph $g$ with $n(g)$ vertices and $m(g)$ edges is obtained from $g$ by replacing every vertex of degree $d$ of $g$ by a clique, which is isomorph to the complete graph $k_{d}$, and each edge $(x_{i},x_{j})$ of $g$ is replaced by an edge $(u,v)$ in such a way that $uin x_{i}$, $vin x_{j}$, and two different edges of $g$ are replaced by non-adjacent edges of $g_{i}$. t...
The Narumi-Katayama index was the first topological index defined by the product of some graph theoretical quantities. Let $G$ be a simple graph with vertex set $V = {v_1,ldots, v_n }$ and $d(v)$ be the degree of vertex $v$ in the graph $G$. The Narumi-Katayama index is defined as $NK(G) = prod_{vin V}d(v)$. In this paper, the Narumi-Katayama index is generalized using a $n$-ve...
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