نتایج جستجو برای: signed petersen graph

تعداد نتایج: 213036  

Journal: :Discrete Mathematics 2002
Randall J. Elzinga David A. Gregory Kevin N. Vander Meulen

Motivated by a problem on message routing in communication networks, Graham and Pollak proposed a scheme for addressing the vertices of a graph G by N -tuples of three symbols in such a way that distances between vertices may readily be determined from their addresses. They observed that N ≥ h(D), the maximum of the number of positive and the number of negative eigenvalues of the distance matri...

Journal: :Ars Mathematica Contemporanea 2022

The total graph is built by joining the to its line means of incidences. We introduce a similar construction for signed graphs. Under two defnitions graph, we defne corresponding and show that it stable under switching. consider balance, frustration index number, largesteigenvalue. In regular case compute spectrum adjacency matrix spectra certain compositions, determine some with exactly main e...

Let $G$ be a graph with vertex set $V(G)$. For any integer $kge 1$, a signed (total) $k$-dominating functionis a function $f: V(G) rightarrow { -1, 1}$ satisfying $sum_{xin N[v]}f(x)ge k$ ($sum_{xin N(v)}f(x)ge k$)for every $vin V(G)$, where $N(v)$ is the neighborhood of $v$ and $N[v]=N(v)cup{v}$. The minimum of the values$sum_{vin V(G)}f(v)$, taken over all signed (total) $k$-dominating functi...

Journal: :Rocky Mountain Journal of Mathematics 2019

Journal: :Bulletin of the Malaysian Mathematical Sciences Society 2015

A graceful labeling of a graph $G=(V,E)$ with $m$ edges is aninjection $f: V(G) rightarrow {0,1,ldots,m}$ such that the resulting edge labelsobtained by $|f(u)-f(v)|$ on every edge $uv$ are pairwise distinct. For natural numbers $n$ and $k$, where $n > 2k$, a generalized Petersengraph $P(n, k)$ is the graph whose vertex set is ${u_1, u_2, cdots, u_n} cup {v_1, v_2, cdots, v_n}$ and its edge set...

Journal: :transactions on combinatorics 2014
veena mathad kishori p. narayankar

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 ...

1998
Marcelo H. Carvalho

In 1987, Lovv asz conjectured that every brick G diierent from K 4 , C 6 , and the Petersen graph has an edge e such that G e is a matching covered graph with exactly one brick. Lovv asz and Vempala announced a proof of this conjecture in 1994. Their paper is under preparation. We present here an independent proof of their theorem. We shall in fact prove that if G is any brick diierent from K 4...

1999
Chi-Hsiang Yeh Behrooz Parhami

The Petersen graph is a Moore graph that has node degree 3, diameter 2, and optimal network size 10. In this paper, we present a class of interconnection networks, called cyclic Petersen networks (CPNs), which efficiently extend the Petersen graph to obtain larger networks with small diameter and node degree. We derive balanced routing algorithms and efficient embeddings for CPNs. In particular...

Journal: :Discrete Mathematics 1992
Gary Chartrand Héctor Hevia Robin J. Wilson

Chartrand, G., H. Hevia and R.J. Wilson, The ubiquitous Petersen graph, Discrete Mathematics 100 (1992) 303-311.

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