For a given simple graph G = (V,E), we define an incidence as a pair (v, e), where vertex v ∈ V (G) is one of the ends of edge e ∈ E(G). Let us define a set of incidences I(G) = {(v, e) : v ∈ V (G)∧ e ∈ E(G)∧ v ∈ e}. We say that two incidences (v, e) and (w, f) are adjacent if one of the following holds: (i) v = w, e 6= f , (ii) e = f , v 6= w, (iii) e = {v, w}, f = {w, u} and v 6= u. By an inc...

De nition. Let (V, 〈 , 〉) be a n-dimensional euclidean vector space and T : V −→ V a linear operator. We will call the adjoint of T , the linear operator S : V −→ V such that: 〈T (u), v〉 = 〈u, S(v)〉 , for all u, v ∈ V . Proposition 1. Let (V, 〈 , 〉) be a n-dimensional euclidean vector space and T : V −→ V a linear operator. The adjoint of T exists and is unique. Moreover, if E denotes an orthon...

If D = (V,A) is a digraph, its niche hypergraph NH(D) = (V, E) has the edge set E = {e ⊆ V | |e| ≥ 2 ∧ ∃v ∈ V : e = N− D (v) ∨ e = N + D (v)}. Niche hypergraphs generalize the well-known niche graphs (cf. [?]) and are closely related to competition hypergraphs (cf. [?]) as well as double competition hypergraphs (cf. [?]). We present several properties of niche hypergraphs of acyclic digraphs.

هدف: هدف از این پژوهش بررسی واسطه‌­ای راهبردهای سازش نایافته تنظیم شناختی هیجان در رابطه باورهای فراشناختی با اضطراب امتحان بود. روش: روش حاضر توصیفی و نوع همبستگی جامعه آماری را کلیه دانش‌­آموزان پسر دوره دوم متوسطه شهر تهران سال تحصیلی 1401-1400 تشکیل دادند که تعداد 456 نفر به نمونه‏‌گیری دسترس انتخاب شرکت کردند. ابزارها شامل سیاهه ابوالقاسمی همکاران (1375)، پرسشنامه باکو دیگران (2009)، فرم ک...

a signed graph (marked graph) is an ordered pair $s=(g,sigma)$$(s=(g,mu))$, where $g=(v,e)$ is a graph called the underlyinggraph of $s$ and $sigma:erightarrow{+,-}$$(mu:vrightarrow{+,-})$ is a function. for a graph $g$, $v(g),e(g)$ and $c(g)$ denote its vertex set, edge set and cut-vertexset, respectively. the lict graph $l_{c}(g)$ of a graph $g=(v,e)$is defined as the graph having vertex set ...

For any vertex v and any edge e in a non-trivial connected graph G, the eccentricity e(v) of v is e(v) =max{d(v, u) : u ∈ V }, the vertex-to-edge eccentricity e1(v) of v is e1(v) = max{d(v, e) : e ∈ E}, the edge-to-vertex eccentricity e2(e) of e is e2(e) = max{d(e, u) : u ∈ V } and the edge-to-edge eccentricity e3(e) of e is e3(e) = max{d(e, f) : f ∈ E}. The set C(G) of all vertices v for which...

1. The average cost of a directed cycle is AvgCost(C) = ω(C) /t = e∈C ω(e) /t. (v) denote the minimum length of a walk with exactly k edges, ending at v. So, for each v, we have d 0 (v) = 0 and d k+1 (v) = min e=(u→v)∈E d k (u) + ω(e) .

a set $s$ of vertices in a graph $g=(v,e)$ is called a total$k$-distance dominating set if every vertex in $v$ is withindistance $k$ of a vertex in $s$. a graph $g$ is total $k$-distancedomination-critical if $gamma_{t}^{k} (g - x) < gamma_{t}^{k}(g)$ for any vertex $xin v(g)$. in this paper,we investigate some results on total $k$-distance domination-critical of graphs.