Weak Balance in Random Signed Graphs
نویسندگان
چکیده
منابع مشابه
Weak Balance in Random Signed Graphs
In this work we deal with questions on balance and weak balance in random graphs. The theory of balance goes back to Heider [12] who asserted that a social system is balanced if there is no tension and that unbalanced social structures exhibit a tension resulting in a tendency to change in the direction of balance. Since this first work of Heider, the notion of balance has been extensively stud...
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By extending Heider’s and Cartwright-Harary’s theory of balance in deterministic social structures, we study the problem of balance in social structures where relations between individuals are random. An appropriate model for representing such structures is the so called random signed graphs Gn,p,q defined as follows. Given a set of n vertices and fixed numbers p and q, 0 < p+ q < 1, then, betw...
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A {em weak signed Roman dominating function} (WSRDF) of a graph $G$ with vertex set $V(G)$ is defined as afunction $f:V(G)rightarrow{-1,1,2}$ having the property that $sum_{xin N[v]}f(x)ge 1$ for each $vin V(G)$, where $N[v]$ is theclosed neighborhood of $v$. The weight of a WSRDF is the sum of its function values over all vertices.The weak signed Roman domination number of $G...
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Let $kge 1$ be an integer, and let $G$ be a finite and simple graph with vertex set $V(G)$.A weak signed Roman $k$-dominating function (WSRkDF) on a graph $G$ is a function$f:V(G)rightarrow{-1,1,2}$ satisfying the conditions that $sum_{xin N[v]}f(x)ge k$ for eachvertex $vin V(G)$, where $N[v]$ is the closed neighborhood of $v$. The weight of a WSRkDF $f$ is$w(f)=sum_{vin V(G)}f(v)$. The weak si...
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ژورنال
عنوان ژورنال: Internet Mathematics
سال: 2014
ISSN: 1542-7951,1944-9488
DOI: 10.1080/15427951.2014.912994