ON MAXIMAL ENERGY AND HOSOYA INDEX OF TREES WITHOUT PERFECT MATCHING
نویسندگان
چکیده
منابع مشابه
Maximal Hosoya index and extremal acyclic molecular graphs without perfect matching
Let T be an acyclic graph without perfect matching and Z(T ) be its Hosoya index; let Fn be the nth Fibonacci number. It is proved in this work that Z(T ) ≤ 2F2m F2m+1 when T has order 4m with the equality holding if and only if T = T1,2m−1,2m−1, and that Z(T ) ≤ F2 2m+2 + F2m F2m+1 when T has order 4m + 2 with the equality holding if and only if T = T1,2m+1,2m−1, where m is a positive integer ...
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Abstract. The energy of a molecular graph is a popular parameter that is defined as the sum of the absolute values of a graph’s eigenvalues. It is well known that the energy is related to the matching polynomial and thus also to the Hosoya index via a certain Coulson integral. Trees minimizing the energy under various additional conditions have been determined in the past, e.g., trees with a gi...
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For a graph G, the Hosoya index and the Merrifield-Simmons index are defined as the total number of its matchings and the total number of its independent sets, respectively. In this paper, we characterize the structure of those graphs that minimize the Merrifield-Simmons index and those that maximize the Hosoya index in two classes of simple connected graphs with n vertices: graphs with fixed m...
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We characterize the trees T with n vertices whose Hosoya index (total number of matchings) is Z(T ) > 16fn−5 resp. the trees whose Merrifield-Simmons index (total number of independent subsets) is σ(T ) < 18fn−5 + 21fn−6, where fk is the kth Fibonacci number. It turns out that all the trees satisfying the inequality are tripodes (trees with exactly three leaves) and the path in both cases. Furt...
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If G is a bridgeless cubic graph, Fulkerson conjectured that we can find 6 perfect matchings M1, . . . ,M6 of G with the property that every edge of G is contained in exactly two of them and Berge conjectured that its edge set can be covered by 5 perfect matchings. We define τ(G) as the least number of perfect matchings allowing to cover the edge set of a bridgeless cubic graph and we study thi...
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ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 2009
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972709000562